Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
565 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 565 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 1. C2×C3×D3×D8 | C2 | semidirect |
| 2. C2×C3×#826 | C2 | semidirect |
| 3. #10590831 | C2 | semidirect |
| 4. C2×#63545 | C2 | semidirect |
| 5. #10589428 | C2 | semidirect |
| 6. #10589115 | C2 | semidirect |
| 7. (C2×D3)⋊(C3⋊C16) | C2 | semidirect |
| 16. C2×C3×D24 | C22 | semidirect |
| 19. #63645 | C22 | semidirect |
| 20. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 22. C2×C3×C3⋊C16 | C22 | semidirect |
| 26. C2×D3×D8 | D3 | semidirect |
| 31. C2×#826 | D3 | semidirect |
| 50. C32×D8 | D4 | semidirect |
| 58. C3×D24 | D4 | semidirect |
| 82. C2×D24 | C2×D3 | semidirect |
| 97. C2×C3⋊C16 | C2×D3 | semidirect |
| 156. C3×D8 | #67 | semidirect |
| 157. C3×D8 | #67 | semidirect |
| 174. D24 | #67 | semidirect |
| 195. C2×C3×D3 | D16 | semidirect |
| 290. D8 | #625 | semidirect |
| 330. C2×D3 | #826 | semidirect |
| 342. C32 | #2184 | semidirect |
| 403. C3 | #71467 | semidirect |
| 404. C3 | #72035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×D8 | 2 |
| C2×C3×#826 | 2 |
| #10590831 | 2 |
| C2×#63545 | 2 |
| #10589428 | 2 |
| #10589115 | 2 |
| (C2×D3)⋊(C3⋊C16) | 2 |
| #72035 | 3 |
| #71467 | 3 |