Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
944 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 163 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×D19 |
| commutator, socle, cosocle | C23×C19 | C24 |
| Fitting | C19×#394 | C2 |
| hypercenter | #394 | D19 |
| hypocenter | C19 | #2388 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #394 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#64543 | C2 | semidirect |
| 2. C2×#10597339 | C2 | semidirect |
| 3. C2×(C22⋊D19)⋊C4 | C2 | semidirect |
| 4. #11926464 | C2 | semidirect |
| 5. #11926459 | C2 | semidirect |
| 6. #11926457 | C2 | semidirect |
| 7. #11926453 | C2 | semidirect |
| 8. #11926452 | C2 | semidirect |
| 9. C22⋊C4×Dic19 | C2 | semidirect |
| 10. #11926391 | C2 | semidirect |
| 11. C19×#394 | C2 | semidirect |
| 56. C22×Dic19 | D4 | semidirect |
| 68. C2×C4×D19 | D4 | semidirect |
| 99. C22×D19 | #41 | semidirect |
| 110. C2×C4×C19 | #41 | semidirect |
| 123. C2×Dic19 | #41 | semidirect |
| 164. #394 | D19 | semidirect |
| 205. C19 | #2388 | semidirect |
| 294. C2×C4 | #64543 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#64543 | 2 |
| C2×#10597339 | 2 |
| C2×(C22⋊D19)⋊C4 | 2 |
| #11926464 | 2 |
| #11926459 | 2 |
| #11926457 | 2 |
| #11926453 | 2 |
| #11926452 | 2 |
| C22⋊C4×Dic19 | 2 |
| #11926391 | 2 |
| C19×#394 | 2 |
| #2388 | 19 |