Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
636 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 214 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D9 |
| commutator | C22×C9 | C23×C4 |
| Frattini, socle, prime radical | C23×C3 | C23×D3 |
| Fitting | C9×#383 | C2 |
| cosocle | C23×C9 | C24 |
| hypercenter | #383 | D9 |
| hypocenter | C9 | #2381 |
| LCS | G ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C23 ◁ #383 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. #63431 | C4 | semidirect |
| 163. C9 | #2381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63431 | 2 |
| C9×#383 | 2 |
| #10588617 | 2 |
| #10588334 | 2 |
| #10588333 | 2 |
| #10588326 | 2 |
| #74265 | 3 |