Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
852 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×Q8×D17 | C2 | semidirect |
| 2. C2×#10587622 | C2 | semidirect |
| 4. #11762721 | C2 | semidirect |
| 5. #11762716 | C2 | semidirect |
| 6. #11762715 | C2 | semidirect |
| 7. #11762685 | C2 | semidirect |
| 8. C4×#63227 | C2 | semidirect |
| 9. C2×C17×#124 | C2 | semidirect |
| 37. C2×Q8×C17 | D4 | semidirect |
| 62. C2×Dic34 | D4 | semidirect |
| 123. C2×D17 | #124 | semidirect |
| 133. C2×#124 | D17 | semidirect |
| 170. C17 | #2436 | semidirect |
| 182. C2×Q8 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D17 | 2 |
| C2×#10587622 | 2 |
| C2×#10587624 | 2 |
| #11762721 | 2 |
| #11762716 | 2 |
| #11762715 | 2 |
| #11762685 | 2 |
| C4×#63227 | 2 |
| C2×C17×#124 | 2 |
| #2436 | 17 |