Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
372 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 4. C22×#11924036 | C4 | semidirect |
| 7. C2×#14556648 | C4 | semidirect |
| 14. #17988356 | C4 | semidirect |
| 15. #343×C73 | C4 | semidirect |
| 172. C73 | #7236 | semidirect |
| 182. #343 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625907 | 2 |
| #22625794 | 2 |
| #22609922 | 2 |
| #7236 | 73 |