Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
366 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 113 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. #11763364 | C2 | semidirect |
| 3. #11763217 | C2 | semidirect |
| 4. #11763172 | C2 | semidirect |
| 5. #11763136 | C2 | semidirect |
| 6. #11763132 | C2 | semidirect |
| 7. #11763100 | C2 | semidirect |
| 8. #11763099 | C2 | semidirect |
| 9. #11763086 | C2 | semidirect |
| 10. #11762865 | C2 | semidirect |
| 11. C17×#474 | C2 | semidirect |
| 142. #474 | D17 | semidirect |
| 181. C17 | #3235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763364 | 2 |
| #11763356 | 2 |
| #11763217 | 2 |
| #11763172 | 2 |
| #11763136 | 2 |
| #11763132 | 2 |
| #11763100 | 2 |
| #11763099 | 2 |
| #11763086 | 2 |
| #11762865 | 2 |
| C17×#474 | 2 |
| #3235 | 17 |