Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
412 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22559000 | C2 | semidirect |
| 5. #22558041 | C2 | semidirect |
| 6. #22558041 | C2 | semidirect |
| 7. C67×#1574 | C2 | semidirect |
| 20. #16863144 | C4 | semidirect |
| 21. #16863144 | C4 | semidirect |
| 22. #16863139 | C4 | semidirect |
| 23. #16863139 | C4 | semidirect |
| 166. #1574 | D67 | semidirect |
| 170. C67 | #8935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569275 | 2 |
| #22561036 | 2 |
| #22559000 | 2 |
| #22558869 | 2 |
| #22558041 | 2 |
| C67×#1574 | 2 |
| #8935 | 67 |