Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1272 conjugacy classes of subgroups; only the 337 normal subgroups are shown.
This group has 1272 conjugacy classes of subgroups — too many to draw. Only its 337 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 | C23×C3⋊D3 |
| commutator | C22×C32 | C23×C4 |
| Fitting | C32×#383 | C2 |
| socle, prime radical, cosocle | C23×C32 | C24 |
| hypercenter | #383 | C3⋊D3 |
| hypocenter | C32 | #2381 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ #383 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. #64078 | C4 | semidirect |
| 163. C32 | #2381 | semidirect |
| 195. C3 | #74265 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64078 | 2 |
| C32×#383 | 2 |
| #10592636 | 2 |
| #10592353 | 2 |
| #10592352 | 2 |
| #10592345 | 2 |
| #74265 | 3 |