Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
568 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 568 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 |
|---|---|---|
| 4. #22558035 | C2 | semidirect |
| 5. #22558033 | C2 | semidirect |
| 6. #22558031 | C2 | semidirect |
| 7. C67×#1272 | C2 | semidirect |
| 210. #1272 | D67 | semidirect |
| 213. C67 | #7681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568550 | 2 |
| #22559901 | 2 |
| #336×D67 | 2 |
| #22558035 | 2 |
| #22558033 | 2 |
| #22558031 | 2 |
| C67×#1272 | 2 |
| #7681 | 67 |