Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
418 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 123 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. #11763196 | C2 | semidirect |
| 3. #11763185 | C2 | semidirect |
| 4. #11763024 | C2 | semidirect |
| 5. #11763006 | C2 | semidirect |
| 6. #11763004 | C2 | semidirect |
| 7. #11763001 | C2 | semidirect |
| 8. #11762940 | C2 | semidirect |
| 9. #11762919 | C2 | semidirect |
| 10. C4×#63229 | C2 | semidirect |
| 11. C17×#550 | C2 | semidirect |
| 108. #3622 | #41 | semidirect |
| 130. #550 | D17 | semidirect |
| 175. C17 | #3399 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763544 | 2 |
| #11763196 | 2 |
| #11763185 | 2 |
| #11763024 | 2 |
| #11763006 | 2 |
| #11763004 | 2 |
| #11763001 | 2 |
| #11762940 | 2 |
| #11762919 | 2 |
| C4×#63229 | 2 |
| C17×#550 | 2 |
| #3399 | 17 |