Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
494 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 3. #22561029 | C2 | semidirect |
| 4. #22558880 | C2 | semidirect |
| 6. #22558068 | C2 | semidirect |
| 7. C67×#1275 | C2 | semidirect |
| 11. #16863801 | C4 | semidirect |
| 12. #16863743 | C4 | semidirect |
| 188. #1275 | D67 | semidirect |
| 189. C67 | #9291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571332 | 2 |
| #22568928 | 2 |
| #22561029 | 2 |
| #22558880 | 2 |
| #22558770 | 2 |
| #22558068 | 2 |
| C67×#1275 | 2 |
| #9291 | 67 |