Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
346 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 79 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. #11763283 | C2 | semidirect |
| 3. #11762825 | C2 | semidirect |
| 4. #11762815 | C2 | semidirect |
| 5. #11762782 | C2 | semidirect |
| 6. #11762566 | C2 | semidirect |
| 7. C17×#344 | C2 | semidirect |
| 17. C2×D136 | C4 | semidirect |
| 18. C2×#63219 | C4 | semidirect |
| 36. C2×D68 | C2×C4 | semidirect |
| 41. C2×Dic34 | C2×C4 | semidirect |
| 47. C2×C8×C17 | C2×C4 | semidirect |
| 115. #344 | D17 | semidirect |
| 140. C17 | #1904 | semidirect |
| 165. C2×C8 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587594 | 2 |
| #11763283 | 2 |
| #11762825 | 2 |
| #11762815 | 2 |
| #11762782 | 2 |
| #11762566 | 2 |
| C17×#344 | 2 |
| #1904 | 17 |