Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
468 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 3. #22625854 | C2 | semidirect |
| 4. #22624808 | C2 | semidirect |
| 19. #17988327 | C4 | semidirect |
| 20. #17988326 | C4 | semidirect |
| 21. #329×C73 | C4 | semidirect |
| 47. #14556502 | C2×C4 | semidirect |
| 50. #97×C73 | C2×C4 | semidirect |
| 164. C73 | #8914 | semidirect |
| 180. #329 | #64408 | semidirect |
| 206. #97 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626474 | 2 |
| #22626061 | 2 |
| #22625854 | 2 |
| #22624808 | 2 |
| #329×D73 | 2 |
| #8914 | 73 |