Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1422 conjugacy classes of subgroups; only the 336 normal subgroups are shown.
This group has 1422 conjugacy classes of subgroups — too many to draw. Only its 336 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. #17988433 | C4 | semidirect |
| 13. #17988433 | C4 | semidirect |
| 14. #17988432 | C4 | semidirect |
| 16. #376×C73 | C4 | semidirect |
| 119. C73 | #13854 | semidirect |
| 128. #376 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C4⋊#64408 | 2 |
| #22625117 | 2 |
| C4×(C2×#64408)⋊C4 | 2 |
| #376×D73 | 2 |
| #13854 | 73 |