Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
200 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 53. Q8×C17 | Q16 | semidirect |
| 108. C17 | #1645 | semidirect |
| 139. Q8 | #63231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763159 | 2 |
| #11763094 | 2 |
| #11763019 | 2 |
| #11762558 | 2 |
| Q8⋊#3622 | 2 |
| Q82×C17 | 2 |
| #1645 | 17 |