Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
324 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 66 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. #11763887 | C2 | semidirect |
| 2. #11763807 | C2 | semidirect |
| 3. #11763801 | C2 | semidirect |
| 4. D17⋊#100 | C2 | semidirect |
| 5. #11763691 | C2 | semidirect |
| 6. #11763678 | C2 | semidirect |
| 17. C2×D8×C17 | C4 | semidirect |
| 18. C2×#63229 | C4 | semidirect |
| 19. C2×#63228 | C4 | semidirect |
| 22. C2×#63219 | C4 | semidirect |
| 140. C2×D8 | #595 | semidirect |
| 152. C17 | #1903 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763887 | 2 |
| #11763807 | 2 |
| #11763801 | 2 |
| D17⋊#100 | 2 |
| #11763691 | 2 |
| #11763678 | 2 |
| C2×#10587597 | 2 |
| #1903 | 17 |