Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11763433 | C2 | semidirect |
| 2. #11763193 | C2 | semidirect |
| 3. #11763171 | C2 | semidirect |
| 4. #11763068 | C2 | semidirect |
| 6. #11763039 | C2 | semidirect |
| 7. #11762920 | C2 | semidirect |
| 8. #11762915 | C2 | semidirect |
| 9. #11762896 | C2 | semidirect |
| 10. #11762763 | C2 | semidirect |
| 11. C17×#498 | C2 | semidirect |
| 107. #498 | D17 | semidirect |
| 148. C17 | #3173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763433 | 2 |
| #11763193 | 2 |
| #11763171 | 2 |
| #11763068 | 2 |
| #11763063 | 2 |
| #11763039 | 2 |
| #11762920 | 2 |
| #11762915 | 2 |
| #11762896 | 2 |
| #11762763 | 2 |
| C17×#498 | 2 |
| #3173 | 17 |