Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
418 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22608679 | C2 | semidirect |
| 3. #22607975 | C2 | semidirect |
| 4. C73×#2150 | C2 | semidirect |
| 15. #17988338 | C22 | semidirect |
| 19. C4⋊C16×C73 | C22 | semidirect |
| 139. #2150 | D73 | semidirect |
| 142. C73 | #11926 | semidirect |
| 155. C4⋊C16 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988971 | 2 |
| #22608679 | 2 |
| #22607975 | 2 |
| C73×#2150 | 2 |
| #11926 | 73 |