Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
528 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 104 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. #22625647 | 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 |
| 51. #14556502 | C2×C4 | semidirect |
| 54. #97×C73 | C2×C4 | semidirect |
| 176. C73 | #8224 | semidirect |
| 194. #329 | #64408 | semidirect |
| 223. #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 |
| #22625647 | 2 |
| D73⋊#329 | 2 |
| #22624808 | 2 |
| #329×D73 | 2 |
| #8224 | 73 |