Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
382 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 8. #17989690 | C4 | semidirect |
| 9. C4⋊#11924040 | C4 | semidirect |
| 117. C73 | #12654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627117 | 2 |
| C2×#17989682 | 2 |
| C2×#64408⋊C16 | 2 |
| #22627002 | 2 |
| #22625589 | 2 |
| #12654 | 73 |