Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
842 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 842 conjugacy classes of subgroups — too many to draw. Only its 235 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 |
|---|---|---|
| 15. C2×#11761612 | Q8 | semidirect |
| 19. C22×C67⋊C8 | Q8 | semidirect |
| 89. C67 | #11391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22559948 | 2 |
| #22559906 | 2 |
| C67×#3458 | 2 |
| #11391 | 67 |