Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
174 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 8. C2×#14556641 | C4 | semidirect |
| 12. #17988421 | C4 | semidirect |
| 15. M64×C73 | C4 | semidirect |
| 81. C73 | #7469 | semidirect |
| 89. M64 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989520 | 2 |
| #22626139 | 2 |
| M64×D73 | 2 |
| #7469 | 73 |