Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
338 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 71 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. D8×Dic22 | C2 | semidirect |
| 2. #13070840 | C2 | semidirect |
| 4. #13067977 | C2 | semidirect |
| 5. #13066672 | C2 | semidirect |
| 6. #13066596 | C2 | semidirect |
| 7. C11×#1331 | C2 | semidirect |
| 66. C11×D8 | SD16 | semidirect |
| 93. #1331 | D11 | semidirect |
| 117. Dic22 | D16 | semidirect |
| 205. D8 | #4314 | semidirect |
| 222. C11 | #12352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×Dic22 | 2 |
| #13070840 | 2 |
| #13070651 | 2 |
| #13067977 | 2 |
| #13066672 | 2 |
| #13066596 | 2 |
| C11×#1331 | 2 |
| #12352 | 11 |