Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
701 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 701 conjugacy classes of subgroups — too many to draw. Only its 96 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. C22×#3745 | C2 | semidirect |
| 2. C3×#5115 | C2 | semidirect |
| 3. C2×#63546 | C2 | semidirect |
| 4. C3×#4549 | C2 | semidirect |
| 5. #10589116 | C2 | semidirect |
| 14. C2×C3×D24 | C22 | semidirect |
| 16. C3×#818 | C22 | semidirect |
| 17. C2×C3×C3⋊C16 | C22 | semidirect |
| 24. #5115 | D3 | semidirect |
| 27. #4549 | D3 | semidirect |
| 43. #3745 | D4 | semidirect |
| 67. C2×D24 | C2×D3 | semidirect |
| 73. #818 | C2×D3 | semidirect |
| 74. C2×C3⋊C16 | C2×D3 | semidirect |
| 150. C22×C32 | D16 | semidirect |
| 261. C22×C3 | D48 | semidirect |
| 262. C22×C3 | #826 | semidirect |
| 291. C32 | #2184 | semidirect |
| 337. C22 | #63546 | semidirect |
| 344. C3 | #69108 | semidirect |
| 345. C3 | #71075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3745 | 2 |
| C3×#5115 | 2 |
| C2×#63546 | 2 |
| C3×#4549 | 2 |
| #10589116 | 2 |
| #71075 | 3 |
| #69108 | 3 |