Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
980 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 980 conjugacy classes of subgroups — too many to draw. Only its 143 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. C2×#17988450 | C2 | semidirect |
| 2. #22609841 | C2 | semidirect |
| 3. C2×#17988321 | C2 | semidirect |
| 4. #22607809 | C2 | semidirect |
| 14. C2×#121×C73 | C4 | semidirect |
| 19. #380×C73 | C4 | semidirect |
| 30. #14556498 | D4 | semidirect |
| 209. C73 | #9158 | semidirect |
| 211. C2×#121 | Dic73 | semidirect |
| 220. #380 | Dic73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988450 | 2 |
| #22609841 | 2 |
| C2×#17988321 | 2 |
| #22607809 | 2 |
| C73×#2847 | 2 |
| #9158 | 73 |