Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
468 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 9. #17989453 | C4 | semidirect |
| 12. C2×C4×#10596831 | C4 | semidirect |
| 14. C2×C4×C8×C73 | C4 | semidirect |
| 26. (C2×#64408)⋊C4 | C8 | semidirect |
| 174. C73 | #7024 | semidirect |
| 180. C2×C4×C8 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625788 | 2 |
| #22625107 | 2 |
| C4×#14556503 | 2 |
| #7024 | 73 |