Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #10597383 |
| commutator, cosocle | C42×C19 | C23 |
| Frattini | C42 | C22×D19 |
| Fitting | C19×#459 | C2 |
| socle | C22×C19 | #120 |
| hypercenter | #459 | D19 |
| hypocenter | C19 | #1625 |
| LCS | G ▷ C42×C19 ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #459 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11927198 | C2 | semidirect |
| 2. #11926890 | C2 | semidirect |
| 3. #11926736 | C2 | semidirect |
| 4. #11926291 | C2 | semidirect |
| 5. D4⋊(C19⋊C8) | C2 | semidirect |
| 6. #11926271 | C2 | semidirect |
| 7. C19×#459 | C2 | semidirect |
| 60. D4×C19 | D8 | semidirect |
| 102. #459 | D19 | semidirect |
| 129. C19 | #1625 | semidirect |
| 170. D4 | #64525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927198 | 2 |
| #11926890 | 2 |
| #11926736 | 2 |
| #11926291 | 2 |
| D4⋊(C19⋊C8) | 2 |
| #11926271 | 2 |
| C19×#459 | 2 |
| #1625 | 19 |