Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
628 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 628 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 |
|---|---|---|
| 12. #17989441 | C4 | semidirect |
| 14. C2×Q8×Dic73 | C4 | semidirect |
| 16. #17988485 | C4 | semidirect |
| 20. C4⋊C4×Dic73 | C4 | semidirect |
| 23. #391×C73 | C4 | semidirect |
| 211. C73 | #8217 | semidirect |
| 217. #391 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625658 | 2 |
| C2×#17989441 | 2 |
| #22625107 | 2 |
| #22624804 | 2 |
| #22612469 | 2 |
| #8217 | 73 |