Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
378 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 4. #22560333 | C2 | semidirect |
| 5. #22558324 | C2 | semidirect |
| 6. #22558303 | C2 | semidirect |
| 7. C67×#2151 | C2 | semidirect |
| 10. #16863519 | C4 | semidirect |
| 144. #2151 | D67 | semidirect |
| 150. C67 | #12829 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569127 | 2 |
| #22561959 | 2 |
| #22561917 | 2 |
| #22560333 | 2 |
| #22558324 | 2 |
| #22558303 | 2 |
| C67×#2151 | 2 |
| #12829 | 67 |