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. #11763426 | C2 | semidirect |
| 2. #11763206 | C2 | semidirect |
| 3. #11763192 | C2 | semidirect |
| 4. #11763167 | C2 | semidirect |
| 5. #11763067 | C2 | semidirect |
| 6. #11763036 | C2 | semidirect |
| 7. #11762921 | C2 | semidirect |
| 8. #11762915 | C2 | semidirect |
| 9. #11762900 | C2 | semidirect |
| 10. #11762767 | C2 | semidirect |
| 148. C17 | #3173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763426 | 2 |
| #11763206 | 2 |
| #11763192 | 2 |
| #11763167 | 2 |
| #11763067 | 2 |
| #11763036 | 2 |
| #11762921 | 2 |
| #11762915 | 2 |
| #11762900 | 2 |
| #11762767 | 2 |
| C17×#469 | 2 |
| #3173 | 17 |