Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
518 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 518 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. #22570158 | C2 | semidirect |
| 4. #22560278 | C2 | semidirect |
| 5. #22558574 | C2 | semidirect |
| 7. C67×#1293 | C2 | semidirect |
| 210. #1293 | D67 | semidirect |
| 211. C67 | #9978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570967 | 2 |
| #22570158 | 2 |
| #22570150 | 2 |
| #22560278 | 2 |
| #22558574 | 2 |
| #22558570 | 2 |
| C67×#1293 | 2 |
| #9978 | 67 |