Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
953 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 953 conjugacy classes of subgroups — too many to draw. Only its 190 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D32 |
| commutator, socle, cosocle | C23×C32 | C24 |
| Fitting | C32×#95 | C22 |
| prime radical | C23×C3×D3 | C23 |
| hypercenter | #95 | D32 |
| hypocenter | C32 | #2401 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ #95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10592347 | C2 | semidirect |
| 3. C3×C3⋊#401 | C2 | semidirect |
| 5. #10591341 | C2 | semidirect |
| 7. #10591241 | C2 | semidirect |
| 32. C3⋊#401 | D3 | semidirect |
| 259. C32 | #2401 | semidirect |
| 303. C3 | #77283 | semidirect |
| 304. C3 | #78409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592347 | 2 |
| C3×#4676 | 2 |
| C3×C3⋊#401 | 2 |
| #10591368 | 2 |
| #10591341 | 2 |
| #10591297 | 2 |
| #10591241 | 2 |
| #78409 | 3 |
| #77283 | 3 |