Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
555 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 555 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #63911 |
| commutator, cosocle | C32×C42 | C23 |
| Frattini | C42 | C2×D32 |
| Fitting | C32×C4×C8 | C22 |
| socle | C22×C32 | #127 |
| hypercenter | C4×C8 | D32 |
| hypocenter | C32 | #1721 |
| LCS | G ▷ C32×C42 ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ C4×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10592392 | C2 | semidirect |
| 2. C3×#4695 | C2 | semidirect |
| 3. #10590350 | C2 | semidirect |
| 4. #10590273 | C2 | semidirect |
| 5. C3×#4455 | C2 | semidirect |
| 21. #4695 | D3 | semidirect |
| 27. #4455 | D3 | semidirect |
| 75. C32×C8 | D8 | semidirect |
| 164. C3×C8 | D24 | semidirect |
| 165. C3×C8 | #213 | semidirect |
| 208. C32 | #1721 | semidirect |
| 221. C8 | #3714 | semidirect |
| 243. C3 | #68094 | semidirect |
| 244. C3 | #71280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592392 | 2 |
| C3×#4695 | 2 |
| #10590350 | 2 |
| #10590273 | 2 |
| C3×#4455 | 2 |
| #71280 | 3 |
| #68094 | 3 |