Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
334 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 12. #16863423 | C4 | semidirect |
| 13. #16863423 | C4 | semidirect |
| 18. C4×#11761612 | C4 | semidirect |
| 19. C2×#14523954 | C4 | semidirect |
| 174. C67 | #12865 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568860 | 2 |
| #22560313 | 2 |
| #22558339 | 2 |
| #22558337 | 2 |
| #22558331 | 2 |
| #22558329 | 2 |
| C67×#1827 | 2 |
| #12865 | 67 |