Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
512 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22570590 | C2 | semidirect |
| 4. #22558934 | C2 | semidirect |
| 6. #22558720 | C2 | semidirect |
| 7. C67×#1300 | C2 | semidirect |
| 186. #1300 | D67 | semidirect |
| 187. C67 | #10098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571214 | 2 |
| #22570590 | 2 |
| #22566145 | 2 |
| #22558934 | 2 |
| #22558806 | 2 |
| #22558720 | 2 |
| C67×#1300 | 2 |
| #10098 | 67 |