Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1546 conjugacy classes of subgroups; only the 355 normal subgroups are shown.
This group has 1546 conjugacy classes of subgroups — too many to draw. Only its 355 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 |
|---|---|---|
| 3. #22560281 | C2 | semidirect |
| 4. #22559941 | C2 | semidirect |
| 8. C2×D4×Dic67 | C4 | semidirect |
| 135. C67 | #20690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863871 | 2 |
| #22562791 | 2 |
| #22560281 | 2 |
| #22559941 | 2 |
| C67×#2309 | 2 |
| #20690 | 67 |