Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
476 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 96. C2×Q8×C67 | Q16 | semidirect |
| 188. C67 | #10183 | semidirect |
| 266. C2×Q8 | #11761618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571154 | 2 |
| C2×#16863691 | 2 |
| #22558895 | 2 |
| #22558612 | 2 |
| #22558533 | 2 |
| #22558104 | 2 |
| C67×#3078 | 2 |
| #10183 | 67 |