Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
198 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #10597330 |
| commutator, cosocle | C42×C19 | C23 |
| Frattini | C42 | C22×D19 |
| Fitting | C19×#331 | C2 |
| socle | C22×C19 | #121 |
| hypercenter | #331 | D19 |
| hypocenter | C19 | #1687 |
| LCS | G ▷ C42×C19 ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #331 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11926920 | C2 | semidirect |
| 2. #11926740 | C2 | semidirect |
| 3. #11926736 | C2 | semidirect |
| 4. #11926621 | C2 | semidirect |
| 5. #11926294 | C2 | semidirect |
| 6. #11926287 | C2 | semidirect |
| 7. C19×#331 | C2 | semidirect |
| 69. C19⋊C8 | D8 | semidirect |
| 93. #331 | D19 | semidirect |
| 115. C19 | #1687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11926920 | 2 |
| #11926740 | 2 |
| #11926736 | 2 |
| #11926621 | 2 |
| #11926294 | 2 |
| #11926287 | 2 |
| C19×#331 | 2 |
| #1687 | 19 |