Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
174 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 6. #17989516 | C4 | semidirect |
| 11. #17988421 | C4 | semidirect |
| 14. M64×C73 | C4 | semidirect |
| 80. C73 | #7478 | semidirect |
| 86. M64 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D73⋊#368 | 2 |
| C2×#17989513 | 2 |
| M64×D73 | 2 |
| #7478 | 73 |