Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
306 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 86 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. #17988415 | C4 | semidirect |
| 20. #17988414 | C4 | semidirect |
| 21. #17988414 | C4 | semidirect |
| 22. #367×C73 | C4 | semidirect |
| 152. C73 | #13111 | semidirect |
| 165. #367 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626035 | 2 |
| #107×#64408 | 2 |
| #22624989 | 2 |
| #22624988 | 2 |
| #22624968 | 2 |
| #367×D73 | 2 |
| #13111 | 73 |