Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
588 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 14. #17988456 | C4 | semidirect |
| 15. #17988456 | C4 | semidirect |
| 21. C4×C4⋊Dic73 | C4 | semidirect |
| 22. C4×C4⋊C4×C73 | C4 | semidirect |
| 198. C73 | #8716 | semidirect |
| 210. C4×C4⋊C4 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625823 | 2 |
| #22625107 | 2 |
| #22624804 | 2 |
| #22612335 | 2 |
| #8716 | 73 |