Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
581 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 581 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×#63653 | C2 | semidirect |
| 3. C3×#5157 | C2 | semidirect |
| 4. C2×C3×#826 | C2 | semidirect |
| 5. #10589116 | C2 | semidirect |
| 6. #10589114 | C2 | semidirect |
| 7. (C2×D3)⋊(C3⋊C16) | C2 | semidirect |
| 11. C2×C32×D8 | C22 | semidirect |
| 20. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 23. C3×#818 | C22 | semidirect |
| 24. C2×C3×C3⋊C16 | C22 | semidirect |
| 29. #5157 | D3 | semidirect |
| 33. C2×#826 | D3 | semidirect |
| 53. #3745 | D4 | semidirect |
| 58. C3×D24 | D4 | semidirect |
| 69. C2×C3×D8 | C2×D3 | semidirect |
| 70. C2×C3×D8 | C2×D3 | semidirect |
| 94. #818 | C2×D3 | semidirect |
| 98. C2×C3⋊C16 | C2×D3 | semidirect |
| 177. D24 | #67 | semidirect |
| 197. C2×C3×D3 | D16 | semidirect |
| 209. C2×D8 | D32 | semidirect |
| 338. C2×D3 | #826 | semidirect |
| 349. C32 | #2184 | semidirect |
| 411. C3 | #71075 | semidirect |
| 412. 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×#63653 | 2 |
| C3×#5157 | 2 |
| C2×C3×#826 | 2 |
| #10589116 | 2 |
| #10589114 | 2 |
| (C2×D3)⋊(C3⋊C16) | 2 |
| #71467 | 3 |
| #71075 | 3 |