Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
500 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22563172 | C2 | semidirect |
| 4. #22558603 | C2 | semidirect |
| 5. #22558112 | C2 | semidirect |
| 6. #22558068 | C2 | semidirect |
| 11. #16863603 | C4 | semidirect |
| 12. #16863593 | C4 | semidirect |
| 205. C67 | #9182 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569677 | 2 |
| #22563172 | 2 |
| #22558769 | 2 |
| #22558603 | 2 |
| #22558112 | 2 |
| #22558068 | 2 |
| C67×#1502 | 2 |
| #9182 | 67 |