Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
284 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 66 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. #11763819 | C2 | semidirect |
| 2. #11763808 | C2 | semidirect |
| 3. #11763807 | C2 | semidirect |
| 4. #11763790 | C2 | semidirect |
| 5. #11763789 | C2 | semidirect |
| 6. #11763772 | C2 | semidirect |
| 14. C2×SD16×C17 | C4 | semidirect |
| 15. C2×#63231 | C4 | semidirect |
| 16. C2×#63228 | C4 | semidirect |
| 21. C2×#63219 | C4 | semidirect |
| 148. C2×SD16 | #595 | semidirect |
| 163. C17 | #1976 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763819 | 2 |
| #11763808 | 2 |
| #11763807 | 2 |
| #11763790 | 2 |
| #11763789 | 2 |
| #11763772 | 2 |
| C2×#10587602 | 2 |
| #1976 | 17 |