Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1038 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1038 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. #10595992 | C2 | semidirect |
| 3. C32×#410 | C2 | semidirect |
| 4. #10592935 | C2 | semidirect |
| 5. #10592700 | C2 | semidirect |
| 6. #10589399 | C2 | semidirect |
| 7. #10589397 | C2 | semidirect |
| 15. C2×#3755 | C4 | semidirect |
| 16. C2×#3753 | C4 | semidirect |
| 28. C3×#410 | D3 | semidirect |
| 38. C2×C32×Q8 | C2×C4 | semidirect |
| 40. C2×C32×D4 | C2×C4 | semidirect |
| 67. C2×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 121. #410 | C3⋊D3 | semidirect |
| 129. C2×C3×Q8 | C4×D3 | semidirect |
| 131. C2×C3×D4 | C4×D3 | semidirect |
| 236. C2×Q8 | C4×C3⋊D3 | semidirect |
| 244. C2×D4 | C4×C3⋊D3 | semidirect |
| 284. C32 | #1904 | semidirect |
| 340. C3 | #70049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64158 | 2 |
| #10595992 | 2 |
| C32×#410 | 2 |
| #10592935 | 2 |
| #10592700 | 2 |
| #10589399 | 2 |
| #10589397 | 2 |
| #70049 | 3 |