Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
380 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 2. #11763219 | C2 | semidirect |
| 3. #11763212 | C2 | semidirect |
| 4. #11763205 | C2 | semidirect |
| 54. #63223 | Q8 | semidirect |
| 74. #3622 | C2×Q8 | semidirect |
| 121. C17 | #3165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587555 | 2 |
| #11763219 | 2 |
| #11763212 | 2 |
| #11763205 | 2 |
| #11762852 | 2 |
| C4×#63223 | 2 |
| C17×#533 | 2 |
| #3165 | 17 |