Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
656 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 261 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 | C23×#384 | C2 |
| socle, cosocle | C23×C23 | C24 |
| prime radical | C23×D23 | C23 |
| hypercenter | #384 | D23 |
| hypocenter | C23 | #2285 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #13092287 | C2 | semidirect |
| 4. #13092282 | C2 | semidirect |
| 6. C4⋊C4×Dic23 | C2 | semidirect |
| 7. C23×#384 | C2 | semidirect |
| 20. C42×D23 | C4 | semidirect |
| 67. C4×D23 | C4⋊C4 | semidirect |
| 81. C4×C23 | #117 | semidirect |
| 88. #384 | D23 | semidirect |
| 112. C23 | #2285 | semidirect |
| 174. C4 | #10625063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625063 | 2 |
| C2×C42×D23 | 2 |
| #13092287 | 2 |
| #13092282 | 2 |
| #13092274 | 2 |
| C4⋊C4×Dic23 | 2 |
| C23×#384 | 2 |
| #2285 | 23 |