Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
338 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 132 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 |
|---|---|---|
| 10. #17989476 | C4 | semidirect |
| 11. C4×#11924031 | C4 | semidirect |
| 14. #17988363 | C4 | semidirect |
| 15. C16×Dic73 | C4 | semidirect |
| 16. #346×C73 | C4 | semidirect |
| 87. C73 | #12593 | semidirect |
| 97. #346 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556666 | 2 |
| #22625587 | 2 |
| #22624971 | 2 |
| #22611524 | 2 |
| #12593 | 73 |