Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1117 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 1117 conjugacy classes of subgroups — too many to draw. Only its 232 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. #10595386 | C2 | semidirect |
| 3. C3×#5184 | C2 | semidirect |
| 4. #10591560 | C2 | semidirect |
| 5. #10591540 | C2 | semidirect |
| 6. #10590768 | C2 | semidirect |
| 7. #10590712 | C2 | semidirect |
| 8. #10590668 | C2 | semidirect |
| 13. #64128 | C4 | semidirect |
| 34. #5184 | D3 | semidirect |
| 44. #3832 | C2×C4 | semidirect |
| 51. C32×Q16 | C2×C4 | semidirect |
| 53. #3755 | C2×C4 | semidirect |
| 55. #3745 | C2×C4 | semidirect |
| 56. C8×C3⋊D3 | C2×C4 | semidirect |
| 148. C3×Q16 | C4×D3 | semidirect |
| 258. Q16 | #624 | semidirect |
| 297. C32 | #2943 | semidirect |
| 338. C3 | #79828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64128 | 2 |
| #10595386 | 2 |
| C3×#5184 | 2 |
| #10591560 | 2 |
| #10591540 | 2 |
| #10590768 | 2 |
| #10590712 | 2 |
| #10590668 | 2 |
| #79828 | 3 |