Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
352 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11763529 | C2 | semidirect |
| 3. #11763207 | C2 | semidirect |
| 4. #11763151 | C2 | semidirect |
| 5. #11763134 | C2 | semidirect |
| 6. #11763105 | C2 | semidirect |
| 7. #11763090 | C2 | semidirect |
| 8. #11763038 | C2 | semidirect |
| 9. C4×#63219 | C2 | semidirect |
| 10. #11762847 | C2 | semidirect |
| 11. C8×D4×C17 | C2 | semidirect |
| 125. C8×D4 | D17 | semidirect |
| 161. C17 | #3340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763529 | 2 |
| #11763524 | 2 |
| #11763207 | 2 |
| #11763151 | 2 |
| #11763134 | 2 |
| #11763105 | 2 |
| #11763090 | 2 |
| #11763038 | 2 |
| C4×#63219 | 2 |
| #11762847 | 2 |
| C8×D4×C17 | 2 |
| #3340 | 17 |