Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
352 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 131 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. #11763518 | C2 | semidirect |
| 2. #11763213 | C2 | semidirect |
| 3. #11763211 | C2 | semidirect |
| 4. #11763210 | C2 | semidirect |
| 5. #11763111 | C2 | semidirect |
| 6. #11763109 | C2 | semidirect |
| 7. #11763097 | C2 | semidirect |
| 8. C8×Dic34 | C2 | semidirect |
| 45. D8×C17 | Q8 | semidirect |
| 147. C17 | #3380 | semidirect |
| 154. D8 | Dic34 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763518 | 2 |
| #11763213 | 2 |
| #11763211 | 2 |
| #11763210 | 2 |
| #11763111 | 2 |
| #11763109 | 2 |
| #11763097 | 2 |
| C8×Dic34 | 2 |
| D8×Dic17 | 2 |
| C4×D8×C17 | 2 |
| #3380 | 17 |