Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
296 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 110 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. #17989476 | C4 | semidirect |
| 14. C4×#11924031 | C4 | semidirect |
| 18. #17988408 | C4 | semidirect |
| 19. #17988407 | C4 | semidirect |
| 20. #364×C73 | C4 | semidirect |
| 114. C73 | #12667 | semidirect |
| 124. #364 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626151 | 2 |
| C4×#14556666 | 2 |
| #22625733 | 2 |
| #22624983 | 2 |
| #364×D73 | 2 |
| #12667 | 73 |