Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
254 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 19. #17988411 | C4 | semidirect |
| 20. #17988410 | C4 | semidirect |
| 21. #17988409 | C4 | semidirect |
| 22. #365×C73 | C4 | semidirect |
| 129. C73 | #13117 | semidirect |
| 142. #365 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626038 | 2 |
| #108×#64408 | 2 |
| #22625013 | 2 |
| #22625009 | 2 |
| #22625000 | 2 |
| #22624974 | 2 |
| #22611702 | 2 |
| #13117 | 73 |