Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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. #11763366 | C2 | semidirect |
| 3. #11763151 | C2 | semidirect |
| 4. #11763105 | C2 | semidirect |
| 5. #11763100 | C2 | semidirect |
| 6. #11763020 | C2 | semidirect |
| 7. #11763015 | C2 | semidirect |
| 9. #11762917 | C2 | semidirect |
| 10. #11762911 | C2 | semidirect |
| 11. C17×#432 | C2 | semidirect |
| 142. #432 | 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 |
|---|---|
| #11763366 | 2 |
| C4×#63252 | 2 |
| #11763151 | 2 |
| #11763105 | 2 |
| #11763100 | 2 |
| #11763020 | 2 |
| #11763015 | 2 |
| #11762973 | 2 |
| #11762917 | 2 |
| #11762911 | 2 |
| C17×#432 | 2 |
| #3116 | 17 |