Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
570 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 17. #17988967 | C4 | semidirect |
| 18. #17988966 | C4 | semidirect |
| 19. #17988966 | C4 | semidirect |
| 22. #494×C73 | C4 | semidirect |
| 65. C4⋊#64408 | Q16 | semidirect |
| 162. C73 | #9066 | semidirect |
| 170. #494 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626464 | 2 |
| #22626109 | 2 |
| D73⋊#333 | 2 |
| #22624766 | 2 |
| #494×D73 | 2 |
| #9066 | 73 |