Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
1160 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 309 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D23 |
| commutator | C22×C23 | C23×C4 |
| Fitting, prime radical | C23×D4×C23 | C2 |
| socle, cosocle | C23×C23 | C24 |
| hypercenter | C23×D4 | D23 |
| hypocenter | C23 | #2308 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C22⋊Dic23 | C2 | semidirect |
| 2. #13092297 | C2 | semidirect |
| 3. #13092280 | C2 | semidirect |
| 4. #13092273 | C2 | semidirect |
| 9. C22×D4×C23 | C4 | semidirect |
| 12. C23×Dic23 | C22 | semidirect |
| 15. C2×C22⋊Dic23 | C22 | semidirect |
| 16. C2×C22⋊Dic23 | C22 | semidirect |
| 17. C23⋊#95 | C22 | semidirect |
| 22. C24×C23 | C2×C4 | semidirect |
| 30. C2×D4×C23 | C2×C4 | semidirect |
| 32. C22×C4×C23 | C2×C4 | semidirect |
| 49. C23×C23 | C22⋊C4 | semidirect |
| 96. C22×D4 | Dic23 | semidirect |
| 105. C23 | #2308 | semidirect |
| 110. C24 | C2×Dic23 | semidirect |
| 118. C2×D4 | C2×Dic23 | semidirect |
| 123. C22×C4 | C2×Dic23 | semidirect |
| 137. C23 | C22⋊Dic23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic23 | 2 |
| #13092297 | 2 |
| #13092280 | 2 |
| #13092273 | 2 |
| C23×D4×C23 | 2 |
| #2308 | 23 |