Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
716 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 198 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. #11763877 | C2 | semidirect |
| 2. #11763790 | C2 | semidirect |
| 3. #11763788 | C2 | semidirect |
| 5. C22×Q8×C17 | C4 | semidirect |
| 7. C2×#63256 | C4 | semidirect |
| 9. C2×Q8×D17 | C4 | semidirect |
| 11. C2×#63252 | C4 | semidirect |
| 88. C22×Q8 | #595 | semidirect |
| 93. C17 | #2884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763877 | 2 |
| #11763790 | 2 |
| #11763788 | 2 |
| C2×#10587694 | 2 |
| #2884 | 17 |