Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1260 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 254 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D9 |
| commutator, cosocle | C23×C9 | C24 |
| Frattini, socle | C23×C3 | C23×D3 |
| Fitting | C9×#376 | C2 |
| hypercenter | #376 | D9 |
| hypocenter | C9 | #2397 |
| LCS | G ▷ C23×C9 ▷ C9 | |
| UCS | C1 ◁ C22×C4 ◁ #376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4×D36 | C2 | semidirect |
| 2. C9×#376 | C2 | semidirect |
| 3. #10588357 | C2 | semidirect |
| 4. #10588351 | C2 | semidirect |
| 24. C42×C9 | D4 | semidirect |
| 48. #376 | D9 | semidirect |
| 96. C42 | D36 | semidirect |
| 105. C9 | #2397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D36 | 2 |
| C9×#376 | 2 |
| #10588357 | 2 |
| #10588351 | 2 |
| #73418 | 3 |