Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
558 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 98 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. #22626156 | C2 | semidirect |
| 2. C2×#17989461 | C2 | semidirect |
| 3. #22624918 | C2 | semidirect |
| 4. #22624917 | C2 | semidirect |
| 8. #17989482 | C22 | semidirect |
| 11. #17989461 | C22 | semidirect |
| 12. C2×D8×D73 | C4 | semidirect |
| 16. #17988823 | C4 | semidirect |
| 20. #107×D73 | C4 | semidirect |
| 22. #466×C73 | C4 | semidirect |
| 33. C2×D584 | C2×C4 | semidirect |
| 49. #14556525 | C2×C4 | semidirect |
| 54. C2×D8×C73 | C2×C4 | semidirect |
| 57. #107×C73 | C2×C4 | semidirect |
| 193. D73 | #1347 | semidirect |
| 199. C73 | C2×#1347 | semidirect |
| 210. #466 | #64408 | semidirect |
| 224. C2×D8 | C2×#64408 | semidirect |
| 248. #107 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626156 | 2 |
| C2×#17989461 | 2 |
| #22624918 | 2 |
| #22624917 | 2 |
| #466×D73 | 2 |
| C2×#1347 | 73 |