Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
570 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 3. #22608502 | C2 | semidirect |
| 4. #22607809 | C2 | semidirect |
| 11. #17988526 | C4 | semidirect |
| 12. #17988523 | C4 | semidirect |
| 13. #17988507 | C4 | semidirect |
| 14. #17988499 | C4 | semidirect |
| 199. C73 | #9383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618955 | 2 |
| #22615107 | 2 |
| #22608502 | 2 |
| #22607809 | 2 |
| C73×#1799 | 2 |
| #9383 | 73 |