Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
434 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 129 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. C4×#63252 | C2 | semidirect |
| 2. #11763130 | C2 | semidirect |
| 3. #11763101 | C2 | semidirect |
| 4. #11763096 | C2 | semidirect |
| 5. #11763006 | C2 | semidirect |
| 6. #11763001 | C2 | semidirect |
| 7. #11762952 | C2 | semidirect |
| 8. C4×#63229 | C2 | semidirect |
| 9. C4×#63228 | C2 | semidirect |
| 10. #11762862 | C2 | semidirect |
| 11. C17×#532 | C2 | semidirect |
| 109. D68 | #41 | semidirect |
| 114. Dic34 | #41 | semidirect |
| 139. #532 | D17 | semidirect |
| 187. C17 | #3106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#63252 | 2 |
| #11763130 | 2 |
| #11763101 | 2 |
| #11763096 | 2 |
| #11763006 | 2 |
| #11763001 | 2 |
| #11762952 | 2 |
| C4×#63229 | 2 |
| C4×#63228 | 2 |
| #11762862 | 2 |
| C17×#532 | 2 |
| #3106 | 17 |