Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
462 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 108. C2×C8×C67 | Q16 | semidirect |
| 177. C67 | #10224 | semidirect |
| 262. C2×C8 | #11761618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571360 | 2 |
| #22571157 | 2 |
| #22570733 | 2 |
| #22558772 | 2 |
| #22558054 | 2 |
| C67×#1993 | 2 |
| #10224 | 67 |