Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
678 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 121 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×Q16×C3⋊D3 | C2 | semidirect |
| 2. C2×C32×SD32 | C2 | semidirect |
| 4. C2×#63654 | C2 | semidirect |
| 5. #10589430 | C2 | semidirect |
| 6. #10589373 | C2 | semidirect |
| 7. #10589369 | C2 | semidirect |
| 25. C2×C3×SD32 | D3 | semidirect |
| 41. C32×Q16 | D4 | semidirect |
| 50. #3746 | D4 | semidirect |
| 94. C2×SD32 | C3⋊D3 | semidirect |
| 109. C3×Q16 | #67 | semidirect |
| 129. C2×C3⋊D3 | SD32 | semidirect |
| 190. Q16 | #638 | semidirect |
| 214. C32 | #2185 | semidirect |
| 254. C3 | #71483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×C3⋊D3 | 2 |
| C2×C32×SD32 | 2 |
| #10592856 | 2 |
| C2×#63654 | 2 |
| #10589430 | 2 |
| #10589373 | 2 |
| #10589369 | 2 |
| #71483 | 3 |