Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
408 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 55 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. #22617639 | C2 | semidirect |
| 2. #22611157 | C2 | semidirect |
| 4. #22607961 | C2 | semidirect |
| 5. #22607935 | C2 | semidirect |
| 6. #22607874 | C2 | semidirect |
| 7. C73×#1604 | C2 | semidirect |
| 196. #1604 | D73 | semidirect |
| 201. C73 | #12145 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22617639 | 2 |
| #22611157 | 2 |
| #22608866 | 2 |
| #22607961 | 2 |
| #22607935 | 2 |
| #22607874 | 2 |
| C73×#1604 | 2 |
| #12145 | 73 |