Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
492 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22561153 | C2 | semidirect |
| 4. #22558720 | C2 | semidirect |
| 6. #22558066 | C2 | semidirect |
| 7. C67×#1300 | C2 | semidirect |
| 11. #16863677 | C4 | semidirect |
| 12. #16863602 | C4 | semidirect |
| 187. #1300 | D67 | semidirect |
| 189. C67 | #9327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570309 | 2 |
| #22562853 | 2 |
| #22561153 | 2 |
| #22558720 | 2 |
| #22558653 | 2 |
| #22558066 | 2 |
| C67×#1300 | 2 |
| #9327 | 67 |