Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
568 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 147 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, socle, cosocle | C23×C23 | C24 |
| Fitting | C23×#393 | C2 |
| prime radical | C22×C22⋊D23 | C22 |
| hypercenter | #393 | D23 |
| hypocenter | C23 | #2398 |
| LCS | G ▷ C23×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ #393 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q8×Dic23 | C2 | semidirect |
| 3. #13092359 | C2 | semidirect |
| 4. #13092344 | C2 | semidirect |
| 5. #13092342 | C2 | semidirect |
| 7. #13092328 | C2 | semidirect |
| 8. C22⋊C4×Dic23 | C2 | semidirect |
| 9. #13092264 | C2 | semidirect |
| 10. #13092262 | C2 | semidirect |
| 11. C23×#393 | C2 | semidirect |
| 139. #393 | D23 | semidirect |
| 175. C23 | #2398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic23 | 2 |
| C2×(C22⋊D23)⋊C4 | 2 |
| #13092359 | 2 |
| #13092344 | 2 |
| #13092342 | 2 |
| #13092333 | 2 |
| #13092328 | 2 |
| C22⋊C4×Dic23 | 2 |
| #13092264 | 2 |
| #13092262 | 2 |
| C23×#393 | 2 |
| #2398 | 23 |