Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
616 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22558761 | C2 | semidirect |
| 5. #22558760 | C2 | semidirect |
| 6. #22558683 | C2 | semidirect |
| 7. C67×#1554 | C2 | semidirect |
| 9. Q8×Dic134 | C4 | semidirect |
| 10. #16864125 | C4 | semidirect |
| 13. #16864119 | C4 | semidirect |
| 15. #16864106 | C4 | semidirect |
| 252. #1554 | D67 | semidirect |
| 258. C67 | #8501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574697 | 2 |
| #22558841 | 2 |
| #22558787 | 2 |
| #22558761 | 2 |
| #22558760 | 2 |
| #22558683 | 2 |
| C67×#1554 | 2 |
| #8501 | 67 |