Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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. #11763179 | C2 | semidirect |
| 3. #11763171 | C2 | semidirect |
| 4. #11763166 | C2 | semidirect |
| 5. #11763161 | C2 | semidirect |
| 6. #11762817 | C2 | semidirect |
| 9. C2×#10587481 | C2 | semidirect |
| 10. #11762765 | C2 | semidirect |
| 11. C17×#544 | C2 | semidirect |
| 123. #544 | D17 | semidirect |
| 168. C17 | #3137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763385 | 2 |
| #11763179 | 2 |
| #11763171 | 2 |
| #11763166 | 2 |
| #11763161 | 2 |
| #11762817 | 2 |
| #11762808 | 2 |
| #11762803 | 2 |
| C2×#10587481 | 2 |
| #11762765 | 2 |
| C17×#544 | 2 |
| #3137 | 17 |