Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
786 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. C67⋊#1304 | C2 | semidirect |
| 7. C2×#117×C67 | C4 | semidirect |
| 9. #379×C67 | C4 | semidirect |
| 103. C67 | #8749 | semidirect |
| 105. C2×#117 | Dic67 | semidirect |
| 109. #379 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22560124 | 2 |
| C67⋊#1304 | 2 |
| C67×#2309 | 2 |
| #8749 | 67 |