Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
396 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 4. #22607950 | C2 | semidirect |
| 5. #22607949 | C2 | semidirect |
| 6. #22607948 | C2 | semidirect |
| 7. C73×#1350 | C2 | semidirect |
| 181. #1350 | D73 | semidirect |
| 182. C73 | #11892 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #467×D73 | 2 |
| C22⋊C16×D73 | 2 |
| #22609968 | 2 |
| #22607950 | 2 |
| #22607949 | 2 |
| #22607948 | 2 |
| C73×#1350 | 2 |
| #11892 | 73 |