Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
2528 conjugacy classes of subgroups; only the 685 normal subgroups are shown.
This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 685 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 | C23×D4×C23 | C2 |
| socle | C24×C23 | C23 |
| hypercenter | C23×D4 | D23 |
| hypocenter | C23 | C22×#121 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C22⋊D23 | C2 | semidirect |
| 2. C23×C22⋊D23 | C2 | semidirect |
| 3. C24×Dic23 | C2 | semidirect |
| 4. C2×#10625110 | C2 | direct (N × H) |
| 5. C22×Dic23⋊C4 | C2 | semidirect |
| 6. C22×C22⋊Dic23 | C2 | semidirect |
| 7. C22×(C2×D23)⋊C4 | C2 | semidirect |
| 8. C23×D4×C23 | C2 | semidirect |
| 13. C22×D4×C23 | C22 | semidirect |
| 17. C22×C22⋊D23 | C22 | semidirect |
| 18. C22×C22⋊D23 | C22 | semidirect |
| 23. C23×Dic23 | C22 | semidirect |
| 24. C2×C22⋊Dic23 | C22 | semidirect |
| 25. #10625110 | C22 | direct (N × H) |
| 26. C2×(C2×D23)⋊C4 | C22 | semidirect |
| 27. C2×Dic23⋊C4 | C22 | semidirect |
| 33. C24×C23 | D4 | semidirect |
| 42. C2×D4×C23 | C23 | semidirect |
| 47. C2×C22⋊D23 | C23 | semidirect |
| 48. C2×C22⋊D23 | C23 | semidirect |
| 52. C22×Dic23 | D4 | semidirect |
| 56. C22×Dic23 | C23 | semidirect |
| 57. C22⋊Dic23 | C23 | semidirect |
| 58. (C2×D23)⋊C4 | C23 | semidirect |
| 59. Dic23⋊C4 | C23 | semidirect |
| 69. C23×C23 | C2×D4 | semidirect |
| 87. C2×Dic23 | C2×D4 | semidirect |
| 99. C22×C23 | #121 | semidirect |
| 102. C22×C23 | C22×D4 | semidirect |
| 112. Dic23 | C22×D4 | semidirect |
| 115. C23×D4 | D23 | semidirect |
| 123. C2×C23 | C2×#121 | semidirect |
| 136. C22×D4 | C2×D23 | semidirect |
| 147. C23 | C22×#121 | semidirect |
| 157. C24 | C22⋊D23 | semidirect |
| 166. C2×D4 | C22×D23 | semidirect |
| 195. C23 | C2×C22⋊D23 | semidirect |
| 222. C22 | #10625110 | direct (N × H) |
| 226. C22 | C22×C22⋊D23 | semidirect |
| 235. C2 | C2×#10625110 | 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 |
| C24×Dic23 | 2 |
| C2×#10625110 | 2 |
| C22×Dic23⋊C4 | 2 |
| C22×C22⋊Dic23 | 2 |
| C22×(C2×D23)⋊C4 | 2 |
| C23×D4×C23 | 2 |
| C22×#121 | 23 |