Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
696 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 217 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. C2×C32×M32 | C2 | semidirect |
| 3. C2×#63645 | C2 | semidirect |
| 4. #10589375 | C2 | semidirect |
| 5. #10589369 | C2 | semidirect |
| 12. #64113 | C4 | semidirect |
| 20. C2×C3×M32 | D3 | semidirect |
| 39. #3746 | C2×C4 | semidirect |
| 41. #3745 | C2×C4 | semidirect |
| 76. C2×M32 | C3⋊D3 | semidirect |
| 179. C32 | #2139 | semidirect |
| 215. C3 | #71439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64113 | 2 |
| C2×C32×M32 | 2 |
| C2×#63645 | 2 |
| #10589375 | 2 |
| #10589369 | 2 |
| #71439 | 3 |