Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
664 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 159 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×D11×Q32 | C2 | semidirect |
| 3. #13070869 | C2 | semidirect |
| 4. #13070708 | C2 | semidirect |
| 5. #13070666 | C2 | semidirect |
| 6. #13070551 | C2 | semidirect |
| 8. C4×C11×Q32 | C2 | semidirect |
| 44. C11×Q32 | D4 | semidirect |
| 97. C4×Q32 | D11 | semidirect |
| 109. D44 | Q32 | direct (N × H) |
| 143. C2×D11 | C2×Q32 | semidirect |
| 147. C4×C11 | C2×Q32 | semidirect |
| 170. Q32 | D44 | direct (N × H) |
| 217. C11 | D4×Q32 | semidirect |
| 248. C4 | D11×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D11×Q32 | 2 |
| Q16×D44 | 2 |
| #13070869 | 2 |
| #13070708 | 2 |
| #13070666 | 2 |
| #13070551 | 2 |
| C16×D44 | 2 |
| C4×C11×Q32 | 2 |
| D4×Q32 | 11 |