Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
274 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 88. C67⋊C8 | Q32 | semidirect |
| 109. C67 | #12528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562462 | 2 |
| #22562461 | 2 |
| #22562438 | 2 |
| #22559825 | 2 |
| #22559807 | 2 |
| #22558128 | 2 |
| C67×#2241 | 2 |
| #12528 | 67 |