Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
714 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 267 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 |
|---|---|---|
| 1. #22560768 | C2 | semidirect |
| 105. C67 | #21913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22560768 | 2 |
| #22560280 | 2 |
| #22560193 | 2 |
| C4×C22⋊(C67⋊C8) | 2 |
| C67×#2296 | 2 |
| #21913 | 67 |