Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
996 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 179 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10595993 | C2 | semidirect |
| 3. C32×#410 | C2 | semidirect |
| 4. C2×#63664 | C2 | semidirect |
| 5. #10592704 | C2 | semidirect |
| 6. #10589399 | C2 | semidirect |
| 7. #10589398 | C2 | semidirect |
| 16. #64151 | C4 | semidirect |
| 17. #64141 | C4 | semidirect |
| 32. C3×#410 | D3 | semidirect |
| 41. C2×C32×Q8 | C2×C4 | semidirect |
| 43. C2×C32×D4 | C2×C4 | semidirect |
| 75. #3748 | C2×C4 | semidirect |
| 139. #410 | C3⋊D3 | semidirect |
| 146. C2×C3×Q8 | C4×D3 | semidirect |
| 148. C2×C3×D4 | C4×D3 | semidirect |
| 272. C2×Q8 | C4×C3⋊D3 | semidirect |
| 276. C2×D4 | C4×C3⋊D3 | semidirect |
| 322. C32 | #1906 | semidirect |
| 382. C3 | #70055 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596293 | 2 |
| #10595993 | 2 |
| C32×#410 | 2 |
| C2×#63664 | 2 |
| #10592704 | 2 |
| #10589399 | 2 |
| #10589398 | 2 |
| #70055 | 3 |