Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1252 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 163 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. #22624336 | C2 | semidirect |
| 2. #22620381 | C2 | semidirect |
| 3. #22609219 | C2 | semidirect |
| 4. #22608523 | C2 | semidirect |
| 5. #22608522 | C2 | semidirect |
| 6. C73×#3151 | C2 | semidirect |
| 8. #17989329 | C22 | semidirect |
| 16. #17988974 | C22 | semidirect |
| 19. C4×#11924012 | C22 | semidirect |
| 20. #17988327 | C22 | semidirect |
| 21. #17988326 | C22 | semidirect |
| 24. C2×#127×C73 | C22 | semidirect |
| 25. #496×C73 | C22 | semidirect |
| 28. C4×M16×C73 | C22 | semidirect |
| 183. #3151 | D73 | semidirect |
| 187. C73 | #19073 | semidirect |
| 199. C2×#127 | C2×D73 | semidirect |
| 201. #496 | C2×D73 | semidirect |
| 207. C4×M16 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22624336 | 2 |
| #22620381 | 2 |
| #22609219 | 2 |
| #22608523 | 2 |
| #22608522 | 2 |
| C73×#3151 | 2 |
| #19073 | 73 |