Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 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. #11763430 | C2 | semidirect |
| 2. #11763207 | C2 | semidirect |
| 3. #11763193 | C2 | semidirect |
| 4. #11763169 | C2 | semidirect |
| 5. #11763067 | C2 | semidirect |
| 7. #11763038 | C2 | semidirect |
| 8. #11762922 | C2 | semidirect |
| 9. #11762917 | C2 | semidirect |
| 10. C4×#63219 | C2 | semidirect |
| 11. C17×#405 | C2 | semidirect |
| 116. #405 | D17 | semidirect |
| 148. C17 | #3173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763430 | 2 |
| #11763207 | 2 |
| #11763193 | 2 |
| #11763169 | 2 |
| #11763067 | 2 |
| #11763062 | 2 |
| #11763038 | 2 |
| #11762922 | 2 |
| #11762917 | 2 |
| C4×#63219 | 2 |
| C17×#405 | 2 |
| #3173 | 17 |