Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
616 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 2. #97×#64408 | C2 | semidirect |
| 4. #22624808 | C2 | semidirect |
| 17. #17989443 | C4 | semidirect |
| 18. #17989442 | C4 | semidirect |
| 21. #17988327 | C4 | semidirect |
| 22. #17988326 | C4 | semidirect |
| 23. #329×C73 | C4 | semidirect |
| 39. #14556646 | C2×C4 | semidirect |
| 53. #14556502 | C2×C4 | semidirect |
| 56. #97×C73 | C2×C4 | semidirect |
| 158. #64408 | #329 | direct (N × H) |
| 178. C73 | C4×#329 | semidirect |
| 196. #329 | #64408 | direct (N × H) |
| 226. #97 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #124×#64408 | 2 |
| #97×#64408 | 2 |
| D73⋊#329 | 2 |
| #22624808 | 2 |
| #329×D73 | 2 |
| C4×#329 | 73 |