Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11763529 | C2 | semidirect |
| 2. #11763155 | C2 | semidirect |
| 3. #11763130 | C2 | semidirect |
| 4. #11763094 | C2 | semidirect |
| 5. #11763036 | C2 | semidirect |
| 6. #11763006 | C2 | semidirect |
| 7. #11762971 | C2 | semidirect |
| 8. C4×#63231 | C2 | semidirect |
| 9. D4×#3622 | C2 | semidirect |
| 10. #11762805 | C2 | semidirect |
| 168. C17 | #3304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763529 | 2 |
| #11763155 | 2 |
| #11763130 | 2 |
| #11763094 | 2 |
| #11763036 | 2 |
| #11763006 | 2 |
| #11762971 | 2 |
| C4×#63231 | 2 |
| D4×#3622 | 2 |
| #11762805 | 2 |
| C17×#550 | 2 |
| #3304 | 17 |