Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
438 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 148 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 |
|---|---|---|
| 13. #17989449 | C4 | semidirect |
| 14. #17989448 | C4 | semidirect |
| 17. #17988338 | C4 | semidirect |
| 18. #17988337 | C4 | semidirect |
| 19. #334×C73 | C4 | semidirect |
| 96. C8×C73 | #97 | semidirect |
| 99. #10596831 | #97 | semidirect |
| 125. C73 | #8273 | semidirect |
| 139. #334 | #64408 | semidirect |
| 219. C8 | #14556645 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625718 | 2 |
| C4×C8×#64408 | 2 |
| #22625473 | 2 |
| #22624760 | 2 |
| #334×D73 | 2 |
| #8273 | 73 |