Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
368 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#10587576 | C2 | semidirect |
| 3. #11763216 | C2 | semidirect |
| 4. #11763172 | C2 | semidirect |
| 5. #11763127 | C2 | semidirect |
| 6. #11763123 | C2 | semidirect |
| 7. #11763120 | C2 | semidirect |
| 8. #11763108 | C2 | semidirect |
| 9. #11763107 | C2 | semidirect |
| 10. #11762863 | C2 | semidirect |
| 11. C17×#481 | C2 | semidirect |
| 134. #481 | D17 | semidirect |
| 177. C17 | #3234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763354 | 2 |
| C2×#10587576 | 2 |
| #11763216 | 2 |
| #11763172 | 2 |
| #11763127 | 2 |
| #11763123 | 2 |
| #11763120 | 2 |
| #11763108 | 2 |
| #11763107 | 2 |
| #11762863 | 2 |
| C17×#481 | 2 |
| #3234 | 17 |