Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×#10587605 | C2 | semidirect |
| 2. C2×#10587593 | C2 | semidirect |
| 3. #11763389 | C2 | semidirect |
| 4. #11763064 | C2 | semidirect |
| 5. #11763063 | C2 | semidirect |
| 6. #11763062 | C2 | semidirect |
| 7. #11763041 | C2 | semidirect |
| 8. #11763040 | C2 | semidirect |
| 9. #106×D17 | C2 | semidirect |
| 10. #11762809 | C2 | semidirect |
| 11. C17×#470 | C2 | semidirect |
| 80. C8×D17 | D4 | semidirect |
| 138. #470 | D17 | semidirect |
| 180. C17 | #3060 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587605 | 2 |
| C2×#10587593 | 2 |
| #11763389 | 2 |
| #11763064 | 2 |
| #11763063 | 2 |
| #11763062 | 2 |
| #11763041 | 2 |
| #11763040 | 2 |
| #106×D17 | 2 |
| #11762809 | 2 |
| C17×#470 | 2 |
| #3060 | 17 |