Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
362 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. #11763208 | C2 | semidirect |
| 3. #11763183 | C2 | semidirect |
| 4. #11763177 | C2 | semidirect |
| 5. #11763175 | C2 | semidirect |
| 6. #11763057 | C2 | semidirect |
| 7. #11763040 | C2 | semidirect |
| 8. #11762907 | C2 | semidirect |
| 9. C4×#63230 | C2 | semidirect |
| 10. #11762765 | C2 | semidirect |
| 11. C17×#541 | C2 | semidirect |
| 105. #541 | D17 | semidirect |
| 147. C17 | #3174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763414 | 2 |
| #11763208 | 2 |
| #11763183 | 2 |
| #11763177 | 2 |
| #11763175 | 2 |
| #11763057 | 2 |
| #11763040 | 2 |
| #11762907 | 2 |
| C4×#63230 | 2 |
| #11762765 | 2 |
| C17×#541 | 2 |
| #3174 | 17 |