Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
366 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 366 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. #11763366 | C2 | semidirect |
| 3. #11763218 | C2 | semidirect |
| 4. #11763203 | C2 | semidirect |
| 5. #11763178 | C2 | semidirect |
| 6. #11763169 | C2 | semidirect |
| 7. #11763050 | C2 | semidirect |
| 9. #11762917 | C2 | semidirect |
| 10. #11762911 | C2 | semidirect |
| 11. C2×C17×#97 | C2 | semidirect |
| 135. C2×#97 | D17 | semidirect |
| 172. C17 | #3181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763366 | 2 |
| #11763343 | 2 |
| #11763218 | 2 |
| #11763203 | 2 |
| #11763178 | 2 |
| #11763169 | 2 |
| #11763050 | 2 |
| #11763038 | 2 |
| #11762917 | 2 |
| #11762911 | 2 |
| C2×C17×#97 | 2 |
| #3181 | 17 |