Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
398 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 134 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. #17989451 | C4 | semidirect |
| 13. #17989450 | C4 | semidirect |
| 17. #17988309 | C4 | semidirect |
| 18. #17988309 | C4 | semidirect |
| 19. #17988308 | C4 | semidirect |
| 20. #322×C73 | C4 | semidirect |
| 91. C8×C73 | #97 | semidirect |
| 95. #10596831 | #97 | semidirect |
| 119. C73 | #8286 | semidirect |
| 134. #322 | #64408 | semidirect |
| 209. C8 | #14556645 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556659 | 2 |
| #22625725 | 2 |
| #22625476 | 2 |
| #22624766 | 2 |
| #322×D73 | 2 |
| #8286 | 73 |