Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
648 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 162 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, cosocle | C23×C9 | C24 |
| Frattini, socle | C23×C3 | C23×D3 |
| Fitting | C9×#401 | C2 |
| prime radical | C23×D9 | C23 |
| hypercenter | #401 | D9 |
| hypocenter | C9 | #2401 |
| LCS | G ▷ C23×C9 ▷ C9 | |
| UCS | C1 ◁ C23 ◁ #401 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C9×#401 | C2 | semidirect |
| 5. #10588338 | C2 | semidirect |
| 6. #10588329 | C2 | semidirect |
| 7. #10588328 | C2 | semidirect |
| 76. #401 | 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×#401 | 2 |
| #10588356 | 2 |
| #10588355 | 2 |
| #10588346 | 2 |
| #10588338 | 2 |
| #10588329 | 2 |
| #10588328 | 2 |
| #78409 | 3 |