Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1066 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1066 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 2. #22620930 | C2 | semidirect |
| 3. #22609236 | C2 | semidirect |
| 4. #22608555 | C2 | semidirect |
| 5. #22608528 | C2 | semidirect |
| 6. C73×#3140 | C2 | semidirect |
| 15. #17988979 | C22 | semidirect |
| 16. #17988949 | C22 | semidirect |
| 20. #17988644 | C22 | semidirect |
| 21. #17988327 | C22 | semidirect |
| 22. #17988326 | C22 | semidirect |
| 23. #533×C73 | C22 | semidirect |
| 25. #489×C73 | C22 | semidirect |
| 29. C4×M16×C73 | C22 | semidirect |
| 58. #14556502 | C23 | semidirect |
| 62. C4⋊Q8×C73 | C23 | semidirect |
| 74. #97×C73 | C23 | semidirect |
| 185. #3140 | D73 | semidirect |
| 189. C73 | #18997 | semidirect |
| 193. #533 | C2×D73 | semidirect |
| 202. #489 | C2×D73 | semidirect |
| 210. C4×M16 | C2×D73 | semidirect |
| 223. C4⋊Q8 | C22×D73 | semidirect |
| 257. #97 | C22×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989329 | 2 |
| #22620930 | 2 |
| #22609236 | 2 |
| #22608555 | 2 |
| #22608528 | 2 |
| C73×#3140 | 2 |
| #18997 | 73 |