Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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. #11763189 | C2 | semidirect |
| 4. #11762554 | C2 | semidirect |
| 5. C17×#335 | C2 | semidirect |
| 39. D68 | Q16 | semidirect |
| 63. #335 | D17 | semidirect |
| 80. C17 | #1669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763189 | 2 |
| #11763090 | 2 |
| C8×D68 | 2 |
| #11762554 | 2 |
| C17×#335 | 2 |
| #1669 | 17 |