Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
372 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 372 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. #11763544 | C2 | semidirect |
| 2. #11763533 | C2 | semidirect |
| 3. #11763194 | C2 | semidirect |
| 4. #11763183 | C2 | semidirect |
| 5. #11763033 | C2 | semidirect |
| 6. #11763027 | C2 | semidirect |
| 8. #11762933 | C2 | semidirect |
| 9. C4×#63230 | C2 | semidirect |
| 10. #11762894 | C2 | semidirect |
| 11. C17×#462 | C2 | semidirect |
| 127. #462 | D17 | semidirect |
| 166. C17 | #3394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763544 | 2 |
| #11763533 | 2 |
| #11763194 | 2 |
| #11763183 | 2 |
| #11763033 | 2 |
| #11763027 | 2 |
| #11763005 | 2 |
| #11762933 | 2 |
| C4×#63230 | 2 |
| #11762894 | 2 |
| C17×#462 | 2 |
| #3394 | 17 |