Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
565 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 565 conjugacy classes of subgroups — too many to draw. Only its 86 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×D3×D24 | C2 | semidirect |
| 2. C2×C3×D48 | C2 | semidirect |
| 3. #10590831 | C2 | semidirect |
| 4. C2×#63546 | C2 | semidirect |
| 5. #10589375 | C2 | semidirect |
| 6. C3×(C2×D3)⋊C16 | C2 | semidirect |
| 7. #10589115 | C2 | semidirect |
| 13. C2×C3×D24 | C22 | semidirect |
| 19. C2×C32×C16 | C22 | semidirect |
| 20. #63645 | C22 | semidirect |
| 21. C2×C3×C3⋊C16 | C22 | semidirect |
| 32. C2×D48 | D3 | semidirect |
| 39. (C2×D3)⋊C16 | D3 | semidirect |
| 52. #3745 | D4 | semidirect |
| 57. C3×D24 | D4 | semidirect |
| 82. C2×D24 | C2×D3 | semidirect |
| 87. C2×C3×C16 | C2×D3 | semidirect |
| 88. C2×C3×C16 | C2×D3 | semidirect |
| 95. C2×C3⋊C16 | C2×D3 | semidirect |
| 174. D24 | #67 | semidirect |
| 194. C2×C3×D3 | D16 | semidirect |
| 212. C2×C16 | D32 | semidirect |
| 330. C2×D3 | D48 | semidirect |
| 342. C32 | #2184 | semidirect |
| 403. C3 | #69108 | semidirect |
| 404. C3 | #71467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×D24 | 2 |
| C2×C3×D48 | 2 |
| #10590831 | 2 |
| C2×#63546 | 2 |
| #10589375 | 2 |
| C3×(C2×D3)⋊C16 | 2 |
| #10589115 | 2 |
| #71467 | 3 |
| #69108 | 3 |