Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
264 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 69 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. #11763922 | C2 | semidirect |
| 2. #11763895 | C2 | semidirect |
| 23. C22×C4×C17 | C8 | semidirect |
| 24. C22×Dic17 | C8 | semidirect |
| 29. C2×C4×D17 | C8 | semidirect |
| 30. C2×C4×D17 | C8 | semidirect |
| 121. C17 | #1458 | semidirect |
| 136. C22×C4 | #3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763922 | 2 |
| #11763895 | 2 |
| #11763894 | 2 |
| C2×#10587677 | 2 |
| #1458 | 17 |