Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
4544 conjugacy classes of subgroups; only the 805 normal subgroups are shown.
This group has 4544 conjugacy classes of subgroups — too many to draw. Only its 805 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D23 |
| commutator, cosocle | C22×C23 | C25 |
| Frattini | C22 | C24×D23 |
| Fitting | C26×C23 | C2 |
| socle | C24×C23 | C23 |
| hypercenter | C26 | D23 |
| hypocenter | C23 | C22×#120 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C24 ◁ C26 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C22⋊D23 | C2 | semidirect |
| 2. C2×#10625124 | C2 | direct (N × H) |
| 3. C22×C22⋊Dic23 | C2 | semidirect |
| 4. C26×C23 | C2 | semidirect |
| 7. C25×C23 | C22 | semidirect |
| 8. C24×D23 | C22 | semidirect |
| 10. C22×C22⋊D23 | C22 | semidirect |
| 11. C23×Dic23 | C22 | semidirect |
| 12. #10625124 | C22 | direct (N × H) |
| 13. C2×C22⋊Dic23 | C22 | semidirect |
| 17. C24×C23 | D4 | semidirect |
| 20. C24×C23 | C23 | semidirect |
| 22. C23×D23 | C23 | semidirect |
| 24. C2×C22⋊D23 | C23 | semidirect |
| 26. C22×Dic23 | C23 | semidirect |
| 27. C22⋊Dic23 | C23 | semidirect |
| 33. C23×C23 | C2×D4 | semidirect |
| 38. C22×D23 | C24 | semidirect |
| 41. C2×Dic23 | C24 | semidirect |
| 46. C22×C23 | #120 | semidirect |
| 48. C22×C23 | C22×D4 | semidirect |
| 53. C26 | D23 | semidirect |
| 58. C2×C23 | C2×#120 | semidirect |
| 64. C25 | C2×D23 | semidirect |
| 70. C23 | C22×#120 | semidirect |
| 76. C24 | C22⋊D23 | semidirect |
| 79. C24 | C22×D23 | semidirect |
| 93. C23 | C2×C22⋊D23 | semidirect |
| 104. C22 | #10625124 | direct (N × H) |
| 106. C22 | C22×C22⋊D23 | semidirect |
| 111. C2 | C2×#10625124 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊D23 | 2 |
| C2×#10625124 | 2 |
| C22×C22⋊Dic23 | 2 |
| C26×C23 | 2 |
| C22×#120 | 23 |