Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
354 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 115 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. #11763115 | C2 | semidirect |
| 4. #11763091 | C2 | semidirect |
| 5. #11763051 | C2 | semidirect |
| 7. #11763030 | C2 | semidirect |
| 8. #11763020 | C2 | semidirect |
| 9. #11763014 | C2 | semidirect |
| 10. C4⋊C8×D17 | C2 | semidirect |
| 11. C17×#474 | C2 | semidirect |
| 133. #474 | D17 | semidirect |
| 176. C17 | #3248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763364 | 2 |
| #11763341 | 2 |
| #11763115 | 2 |
| #11763091 | 2 |
| #11763051 | 2 |
| #11763037 | 2 |
| #11763030 | 2 |
| #11763020 | 2 |
| #11763014 | 2 |
| C4⋊C8×D17 | 2 |
| C17×#474 | 2 |
| #3248 | 17 |