Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
166 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 56 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. Q8×#3624 | C2 | semidirect |
| 3. #11763672 | C2 | semidirect |
| 4. Q8⋊#3624 | C2 | semidirect |
| 6. #11763651 | C2 | semidirect |
| 43. Q8×C17 | M16 | semidirect |
| 100. C17 | #1588 | semidirect |
| 121. Q8 | #63243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#3624 | 2 |
| #11763843 | 2 |
| #11763672 | 2 |
| Q8⋊#3624 | 2 |
| #11763657 | 2 |
| #11763651 | 2 |
| #11762894 | 2 |
| #1588 | 17 |