Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 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. #11763533 | C2 | semidirect |
| 3. #11763146 | C2 | semidirect |
| 4. #11763136 | C2 | semidirect |
| 5. #11763091 | C2 | semidirect |
| 6. #11763086 | C2 | semidirect |
| 7. #11763056 | C2 | semidirect |
| 8. C4×#63219 | C2 | semidirect |
| 9. #11762888 | C2 | semidirect |
| 10. #11762850 | C2 | semidirect |
| 11. C17×#500 | C2 | semidirect |
| 98. C8×C17 | #41 | semidirect |
| 120. #500 | D17 | semidirect |
| 163. C17 | #3353 | semidirect |
| 222. C8 | #63256 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763533 | 2 |
| #11763462 | 2 |
| #11763146 | 2 |
| #11763136 | 2 |
| #11763091 | 2 |
| #11763086 | 2 |
| #11763056 | 2 |
| C4×#63219 | 2 |
| #11762888 | 2 |
| #11762850 | 2 |
| C17×#500 | 2 |
| #3353 | 17 |