Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
190 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 56 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 |
|---|---|---|
| 12. Dic1168 | C4 | semidirect |
| 13. #17988427 | C4 | semidirect |
| 15. Q64×C73 | C4 | semidirect |
| 56. #64408 | Q64 | direct (N × H) |
| 70. C73 | C4×Q64 | semidirect |
| 75. Q64 | #64408 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q32×#64408 | 2 |
| #22625092 | 2 |
| #22625081 | 2 |
| C32×#64408 | 2 |
| Q64×D73 | 2 |
| C4×Q64 | 73 |