Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
684 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 124 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. #22625718 | C2 | semidirect |
| 4. #22624810 | C2 | semidirect |
| 15. #17989445 | C4 | semidirect |
| 18. #17988331 | C4 | semidirect |
| 19. #17988330 | C4 | semidirect |
| 20. #331×C73 | C4 | semidirect |
| 34. #14556658 | C2×C4 | semidirect |
| 44. C4⋊#10596831 | C2×C4 | semidirect |
| 47. C4⋊C8×C73 | C2×C4 | semidirect |
| 164. C73 | #8231 | semidirect |
| 179. #331 | #64408 | semidirect |
| 205. C4⋊C8 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #127×#64408 | 2 |
| #22625718 | 2 |
| D73⋊#331 | 2 |
| #22624810 | 2 |
| #331×D73 | 2 |
| #8231 | 73 |