Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
360 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 28. #14524043 | Q8 | semidirect |
| 29. #14524043 | Q8 | semidirect |
| 172. C67 | #10379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22565857 | 2 |
| #22561153 | 2 |
| #22558761 | 2 |
| #22558720 | 2 |
| #22558074 | 2 |
| #22558064 | 2 |
| C67×#1300 | 2 |
| #10379 | 67 |