Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
354 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 10. #17989475 | C4 | semidirect |
| 11. #17989473 | C4 | semidirect |
| 14. #17988363 | C4 | semidirect |
| 15. C16×Dic73 | C4 | semidirect |
| 16. #346×C73 | C4 | semidirect |
| 88. C73 | #12594 | semidirect |
| 98. #346 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626138 | 2 |
| C4×#14556645 | 2 |
| #22624971 | 2 |
| #22611524 | 2 |
| #12594 | 73 |