Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
458 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22611596 | C2 | semidirect |
| 3. #22608093 | C2 | semidirect |
| 4. C73×#2126 | C2 | semidirect |
| 7. C2×#14556588 | C4 | semidirect |
| 11. #17988961 | C4 | semidirect |
| 13. C4×#11924012 | C4 | semidirect |
| 15. #17988380 | C22 | semidirect |
| 19. #353×C73 | C22 | semidirect |
| 160. #2126 | D73 | semidirect |
| 162. C73 | #13585 | semidirect |
| 177. #353 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620384 | 2 |
| #22611596 | 2 |
| #22608093 | 2 |
| C73×#2126 | 2 |
| #13585 | 73 |