Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
654 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 147 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. #22563299 | C2 | semidirect |
| 4. #22558048 | C2 | semidirect |
| 5. C2×#333×C67 | C2 | semidirect |
| 9. #16863770 | C4 | semidirect |
| 70. C4⋊Dic67 | SD16 | semidirect |
| 153. C2×#333 | D67 | semidirect |
| 155. C67 | #9063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863770 | 2 |
| #22563299 | 2 |
| #22561135 | 2 |
| #22558048 | 2 |
| C2×#333×C67 | 2 |
| #9063 | 67 |