Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
494 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22561030 | C2 | semidirect |
| 5. #22558069 | C2 | semidirect |
| 6. #22558039 | C2 | semidirect |
| 7. C67×#1546 | C2 | semidirect |
| 10. #16863799 | C4 | semidirect |
| 11. #16863744 | C4 | semidirect |
| 185. #1546 | 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 |
|---|---|
| #22571330 | 2 |
| #22568926 | 2 |
| #22561030 | 2 |
| #22558770 | 2 |
| #22558069 | 2 |
| #22558039 | 2 |
| C67×#1546 | 2 |
| #9291 | 67 |