Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 175 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. #11763288 | C2 | semidirect |
| 3. #11762921 | C2 | semidirect |
| 4. #11762917 | C2 | semidirect |
| 5. #11762915 | C2 | semidirect |
| 6. #11762900 | C2 | semidirect |
| 7. C4×#63229 | C2 | semidirect |
| 8. #106×D17 | C2 | semidirect |
| 9. #11762807 | C2 | semidirect |
| 10. #11762766 | C2 | semidirect |
| 11. C17×#442 | C2 | semidirect |
| 19. #10587598 | C4 | semidirect |
| 46. #63254 | C2×C4 | semidirect |
| 50. D8×C17 | C2×C4 | semidirect |
| 57. #63229 | C2×C4 | semidirect |
| 69. Dic68 | C2×C4 | semidirect |
| 71. C8×D17 | C2×C4 | semidirect |
| 114. #442 | D17 | semidirect |
| 154. C17 | #2952 | semidirect |
| 167. D8 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587598 | 2 |
| #11763288 | 2 |
| #11762921 | 2 |
| #11762917 | 2 |
| #11762915 | 2 |
| #11762900 | 2 |
| C4×#63229 | 2 |
| #106×D17 | 2 |
| #11762807 | 2 |
| #11762766 | 2 |
| C17×#442 | 2 |
| #2952 | 17 |