Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
500 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 16. #17989498 | C4 | semidirect |
| 17. #17989497 | C4 | semidirect |
| 21. #17988386 | C4 | semidirect |
| 22. #17988385 | C4 | semidirect |
| 23. #356×C73 | C4 | semidirect |
| 154. #64408 | #356 | direct (N × H) |
| 174. C73 | C4×#356 | semidirect |
| 191. #356 | #64408 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×#64408 | 2 |
| D73⋊#356 | 2 |
| #101×#64408 | 2 |
| #22625027 | 2 |
| #356×D73 | 2 |
| C4×#356 | 73 |