Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 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. #11763437 | C2 | semidirect |
| 3. #11763176 | C2 | semidirect |
| 4. #11763170 | C2 | semidirect |
| 5. #11763165 | C2 | semidirect |
| 6. #11763158 | C2 | semidirect |
| 9. C2×#10587506 | C2 | semidirect |
| 10. #11762767 | C2 | semidirect |
| 11. C17×#419 | C2 | semidirect |
| 129. #419 | D17 | semidirect |
| 168. C17 | #3137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763437 | 2 |
| #11763383 | 2 |
| #11763176 | 2 |
| #11763170 | 2 |
| #11763165 | 2 |
| #11763158 | 2 |
| #11762811 | 2 |
| #11762803 | 2 |
| C2×#10587506 | 2 |
| #11762767 | 2 |
| C17×#419 | 2 |
| #3137 | 17 |