Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
484 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 135 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. C2×#10587595 | C2 | semidirect |
| 2. C2×#10587637 | C2 | semidirect |
| 4. C2×#10587573 | C2 | semidirect |
| 5. #11763034 | C2 | semidirect |
| 6. #11763030 | C2 | semidirect |
| 7. #11763018 | C2 | semidirect |
| 8. #11763008 | C2 | semidirect |
| 9. #11762832 | C2 | semidirect |
| 10. #11762808 | C2 | semidirect |
| 11. C17×#417 | C2 | semidirect |
| 65. C2×Dic34 | D4 | semidirect |
| 151. Dic17 | #137 | semidirect |
| 162. #417 | D17 | semidirect |
| 202. C17 | #3037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587595 | 2 |
| C2×#10587637 | 2 |
| #11763355 | 2 |
| C2×#10587573 | 2 |
| #11763034 | 2 |
| #11763030 | 2 |
| #11763018 | 2 |
| #11763008 | 2 |
| #11762832 | 2 |
| #11762808 | 2 |
| C17×#417 | 2 |
| #3037 | 17 |