Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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. #11763103 | C2 | semidirect |
| 4. #11763101 | C2 | semidirect |
| 7. #11763020 | C2 | semidirect |
| 8. #11763019 | C2 | semidirect |
| 9. #11763018 | C2 | semidirect |
| 11. C17×#477 | C2 | semidirect |
| 100. C4×D17 | Q16 | semidirect |
| 130. #477 | D17 | semidirect |
| 172. C17 | #3249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763364 | 2 |
| #11763363 | 2 |
| #11763103 | 2 |
| #11763101 | 2 |
| #11763051 | 2 |
| #11763049 | 2 |
| #11763020 | 2 |
| #11763019 | 2 |
| #11763018 | 2 |
| C4⋊C8×D17 | 2 |
| C17×#477 | 2 |
| #3249 | 17 |