Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11763545 | C2 | semidirect |
| 2. #11763516 | C2 | semidirect |
| 3. #11763162 | C2 | semidirect |
| 4. #11763155 | C2 | semidirect |
| 5. #11763107 | C2 | semidirect |
| 6. #11763105 | C2 | semidirect |
| 7. #11763022 | C2 | semidirect |
| 8. #11762933 | C2 | semidirect |
| 9. C4×#63229 | C2 | semidirect |
| 10. D8×Dic17 | C2 | semidirect |
| 163. C17 | #3361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763545 | 2 |
| #11763516 | 2 |
| #11763162 | 2 |
| #11763155 | 2 |
| #11763107 | 2 |
| #11763105 | 2 |
| #11763022 | 2 |
| #11762933 | 2 |
| C4×#63229 | 2 |
| D8×Dic17 | 2 |
| C17×#459 | 2 |
| #3361 | 17 |