Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
384 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 82 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. D73⋊#365 | C2 | semidirect |
| 4. #22626048 | C2 | semidirect |
| 5. #22625008 | C2 | semidirect |
| 6. #22624983 | C2 | semidirect |
| 25. #17988404 | C4 | semidirect |
| 26. #17988402 | C4 | semidirect |
| 27. #17988400 | C4 | semidirect |
| 28. #361×C73 | C4 | semidirect |
| 169. C73 | #12952 | semidirect |
| 188. #361 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626707 | 2 |
| D73⋊#365 | 2 |
| C2×#17989503 | 2 |
| #22626048 | 2 |
| #22625008 | 2 |
| #22624983 | 2 |
| #22611677 | 2 |
| #12952 | 73 |