Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
644 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 644 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. #22560144 | C2 | semidirect |
| 5. #22558114 | C2 | semidirect |
| 6. #22558085 | C2 | semidirect |
| 7. C67×#1784 | C2 | semidirect |
| 11. #16863552 | C4 | semidirect |
| 13. #16863535 | C4 | semidirect |
| 254. #1784 | D67 | semidirect |
| 258. C67 | #9519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569443 | 2 |
| #22569259 | 2 |
| #22560144 | 2 |
| #22558753 | 2 |
| #22558114 | 2 |
| #22558085 | 2 |
| C67×#1784 | 2 |
| #9519 | 67 |