Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 3. #11763093 | C2 | semidirect |
| 4. #11763091 | C2 | semidirect |
| 7. #11763020 | C2 | semidirect |
| 8. #11763019 | C2 | semidirect |
| 9. #11763018 | C2 | semidirect |
| 11. C17×#475 | C2 | semidirect |
| 130. #475 | D17 | semidirect |
| 172. C17 | #3255 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763364 | 2 |
| #11763363 | 2 |
| #11763093 | 2 |
| #11763091 | 2 |
| #11763068 | 2 |
| #11763066 | 2 |
| #11763020 | 2 |
| #11763019 | 2 |
| #11763018 | 2 |
| #11762831 | 2 |
| C17×#475 | 2 |
| #3255 | 17 |