Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
648 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 182 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 |
| prime radical | C23×D9 | C23 |
| hypercenter | #376 | D9 |
| hypocenter | C9 | #2401 |
| 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. C9×#376 | C2 | semidirect |
| 3. C4×Dic9⋊C4 | C2 | semidirect |
| 6. C9⋊#401 | C2 | semidirect |
| 7. #10588338 | C2 | semidirect |
| 82. #376 | D9 | semidirect |
| 171. C9 | #2401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#376 | 2 |
| C4×(C2×D9)⋊C4 | 2 |
| C4×Dic9⋊C4 | 2 |
| #10588356 | 2 |
| #10588355 | 2 |
| C9⋊#401 | 2 |
| #10588338 | 2 |
| #73420 | 3 |