Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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. #11763575 | C2 | semidirect |
| 3. #11762825 | C2 | semidirect |
| 4. #11762806 | C2 | semidirect |
| 5. #11762775 | C2 | semidirect |
| 6. #11762581 | C2 | semidirect |
| 7. C17×#341 | C2 | semidirect |
| 16. #10587595 | C4 | semidirect |
| 18. #10587594 | C4 | semidirect |
| 119. #341 | D17 | semidirect |
| 145. C17 | #1881 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763609 | 2 |
| #11763575 | 2 |
| #11762825 | 2 |
| #11762806 | 2 |
| #11762775 | 2 |
| #11762581 | 2 |
| C17×#341 | 2 |
| #1881 | 17 |