Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
454 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 1. #22626224 | C2 | semidirect |
| 2. #22626204 | C2 | semidirect |
| 3. #22625058 | C2 | semidirect |
| 8. #17989496 | C22 | semidirect |
| 9. #17989494 | C22 | semidirect |
| 14. #17988974 | C4 | semidirect |
| 18. C4×#11924012 | C4 | semidirect |
| 19. C2×#127×C73 | C4 | semidirect |
| 161. C73 | #13579 | semidirect |
| 165. C2×#127 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626224 | 2 |
| #22626204 | 2 |
| #22625058 | 2 |
| #22620381 | 2 |
| #13579 | 73 |