Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
212 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 84. C8×C67 | Q32 | semidirect |
| 109. C67 | #12488 | semidirect |
| 187. C8 | #14523989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562358 | 2 |
| #22562256 | 2 |
| #22559107 | 2 |
| #22558279 | 2 |
| #22558267 | 2 |
| #22558258 | 2 |
| C67×#1707 | 2 |
| #12488 | 67 |