Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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×#10587574 | C2 | semidirect |
| 3. #11763216 | C2 | semidirect |
| 4. #11763170 | C2 | semidirect |
| 5. #11763137 | C2 | semidirect |
| 8. #11763102 | C2 | semidirect |
| 9. #11763098 | C2 | semidirect |
| 10. #11762863 | C2 | semidirect |
| 11. C17×#483 | C2 | semidirect |
| 129. #483 | D17 | semidirect |
| 171. C17 | #3238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587574 | 2 |
| #11763345 | 2 |
| #11763216 | 2 |
| #11763170 | 2 |
| #11763137 | 2 |
| #11763123 | 2 |
| #11763122 | 2 |
| #11763102 | 2 |
| #11763098 | 2 |
| #11762863 | 2 |
| C17×#483 | 2 |
| #3238 | 17 |