Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
386 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 119 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. #11763364 | C2 | semidirect |
| 3. #11763152 | C2 | semidirect |
| 4. #11763096 | C2 | semidirect |
| 5. #11763019 | C2 | semidirect |
| 6. #11763015 | C2 | semidirect |
| 8. #11762913 | C2 | semidirect |
| 9. #11762908 | C2 | semidirect |
| 10. #11762865 | C2 | semidirect |
| 11. C17×#477 | C2 | semidirect |
| 135. #477 | D17 | semidirect |
| 179. C17 | #3116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763364 | 2 |
| C4×#63256 | 2 |
| #11763152 | 2 |
| #11763096 | 2 |
| #11763019 | 2 |
| #11763015 | 2 |
| #11762974 | 2 |
| #11762913 | 2 |
| #11762908 | 2 |
| #11762865 | 2 |
| C17×#477 | 2 |
| #3116 | 17 |