Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
412 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 86 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. #22626273 | C2 | semidirect |
| 4. #22625851 | C2 | semidirect |
| 5. #22625013 | C2 | semidirect |
| 6. #22624998 | C2 | semidirect |
| 20. #17988700 | C4 | semidirect |
| 21. #17988699 | C4 | semidirect |
| 22. #17988698 | C4 | semidirect |
| 28. #442×C73 | C4 | semidirect |
| 191. C73 | #12826 | semidirect |
| 199. #442 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626273 | 2 |
| D73⋊#361 | 2 |
| #22626240 | 2 |
| #22625851 | 2 |
| #22625013 | 2 |
| #22624998 | 2 |
| #22618780 | 2 |
| #12826 | 73 |