Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 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. #11763463 | C2 | semidirect |
| 2. #11763155 | C2 | semidirect |
| 3. #11763125 | C2 | semidirect |
| 4. #11763094 | C2 | semidirect |
| 5. #11763060 | C2 | semidirect |
| 6. #11763001 | C2 | semidirect |
| 7. #11762954 | C2 | semidirect |
| 8. C4×#63230 | C2 | semidirect |
| 9. #11762887 | C2 | semidirect |
| 10. #11762810 | C2 | semidirect |
| 11. C17×#550 | C2 | semidirect |
| 81. Q8×C17 | #41 | semidirect |
| 129. #550 | D17 | semidirect |
| 175. C17 | #3332 | semidirect |
| 217. Q8 | #63254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763463 | 2 |
| #11763155 | 2 |
| #11763125 | 2 |
| #11763094 | 2 |
| #11763060 | 2 |
| #11763001 | 2 |
| #11762954 | 2 |
| C4×#63230 | 2 |
| #11762887 | 2 |
| #11762810 | 2 |
| C17×#550 | 2 |
| #3332 | 17 |