Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
1362 conjugacy classes of subgroups; only the 503 normal subgroups are shown.
This group has 1362 conjugacy classes of subgroups — too many to draw. Only its 503 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D23 |
| commutator, cosocle | C2×C23 | C25 |
| Frattini | C2 | C24×D23 |
| Fitting | C22×D4×C23 | C2 |
| socle | C23×C23 | C23 |
| hypercenter | C22×D4 | D23 |
| hypocenter | C23 | C23×D4 |
| LCS | G ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×D23 | C2 | semidirect |
| 2. C22×D4×C23 | C2 | semidirect |
| 3. C22×C22⋊D23 | C2 | semidirect |
| 4. C2×D4×D23 | C2 | direct (N × H) |
| 5. C22×D92 | C2 | semidirect |
| 6. C22×C4×D23 | C2 | semidirect |
| 7. C24×C23 | C22 | semidirect |
| 10. C23×D23 | C22 | semidirect |
| 11. C23×D23 | C22 | semidirect |
| 12. C2×D4×C23 | C22 | semidirect |
| 13. C22×C4×C23 | C22 | semidirect |
| 14. C2×C22⋊D23 | C22 | semidirect |
| 15. C22×Dic23 | C22 | semidirect |
| 16. D4×D23 | C22 | direct (N × H) |
| 17. C2×D92 | C22 | semidirect |
| 18. C2×C4×D23 | C22 | semidirect |
| 21. C23×C23 | C23 | semidirect |
| 24. C22×D23 | D4 | direct (N × H) |
| 26. C22×D23 | C23 | semidirect |
| 27. C22×D23 | C23 | semidirect |
| 28. D4×C23 | C23 | semidirect |
| 29. C2×C4×C23 | C23 | semidirect |
| 30. C22⋊D23 | C23 | semidirect |
| 31. C2×Dic23 | C23 | semidirect |
| 32. D92 | C23 | semidirect |
| 33. C4×D23 | C23 | semidirect |
| 35. C22×C23 | C2×D4 | semidirect |
| 37. C22×C23 | C24 | semidirect |
| 40. C2×D23 | C2×D4 | direct (N × H) |
| 42. C2×D23 | C24 | semidirect |
| 43. C4×C23 | C24 | semidirect |
| 44. Dic23 | C24 | semidirect |
| 47. C2×C23 | C22×D4 | semidirect |
| 50. D23 | C22×D4 | direct (N × H) |
| 55. C22×D4 | D23 | direct (N × H) |
| 57. C23 | C23×D4 | semidirect |
| 62. C24 | C2×D23 | semidirect |
| 66. C2×D4 | C2×D23 | direct (N × H) |
| 69. C22×C4 | C2×D23 | semidirect |
| 78. C23 | C22×D23 | semidirect |
| 81. D4 | C22×D23 | direct (N × H) |
| 84. C2×C4 | C22×D23 | semidirect |
| 91. C22 | D4×D23 | direct (N × H) |
| 93. C22 | C23×D23 | semidirect |
| 95. C4 | C23×D23 | semidirect |
| 99. C2 | C2×D4×D23 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×D23 | 2 |
| C22×D4×C23 | 2 |
| C22×C22⋊D23 | 2 |
| C2×D4×D23 | 2 |
| C22×D92 | 2 |
| C22×C4×D23 | 2 |
| C23×D4 | 23 |