Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
316 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 51 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. #11763434 | C2 | semidirect |
| 2. #11762962 | C2 | semidirect |
| 3. #11762959 | C2 | semidirect |
| 5. #11762545 | C2 | semidirect |
| 6. #11762532 | C2 | semidirect |
| 7. C17×#328 | C2 | semidirect |
| 29. C2×Q8×C17 | D4 | semidirect |
| 42. C2×Dic34 | D4 | semidirect |
| 45. C4⋊C4×C17 | D4 | semidirect |
| 55. C4⋊Dic17 | D4 | semidirect |
| 73. C22×D17 | SD16 | semidirect |
| 129. #328 | D17 | semidirect |
| 157. C17 | #1596 | semidirect |
| 162. C2×Q8 | D68 | semidirect |
| 184. C4⋊C4 | D68 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763434 | 2 |
| #11762962 | 2 |
| #11762959 | 2 |
| #11762719 | 2 |
| #11762545 | 2 |
| #11762532 | 2 |
| C17×#328 | 2 |
| #1596 | 17 |