Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
346 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 89 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. #11762827 | C2 | semidirect |
| 3. #11762814 | C2 | semidirect |
| 4. #11762782 | C2 | semidirect |
| 5. #11762579 | C2 | semidirect |
| 6. #11762565 | C2 | semidirect |
| 7. C17×#518 | C2 | semidirect |
| 15. C2×#63229 | C4 | semidirect |
| 18. C2×#63228 | C4 | semidirect |
| 39. C2×D68 | C2×C4 | semidirect |
| 41. C2×Dic34 | C2×C4 | semidirect |
| 59. C2×#3622 | C2×C4 | semidirect |
| 111. #518 | D17 | semidirect |
| 140. C17 | #1904 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587618 | 2 |
| #11762827 | 2 |
| #11762814 | 2 |
| #11762782 | 2 |
| #11762579 | 2 |
| #11762565 | 2 |
| C17×#518 | 2 |
| #1904 | 17 |