Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
544 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 32. C2×C4⋊Dic67 | Q8 | semidirect |
| 194. C67 | #10343 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22566323 | 2 |
| #22560300 | 2 |
| #22558478 | 2 |
| #22558089 | 2 |
| C67×#1280 | 2 |
| #10343 | 67 |