Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
776 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 776 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 1. #22609919 | C2 | semidirect |
| 2. #22608252 | C2 | semidirect |
| 3. #22607928 | C2 | semidirect |
| 8. #17988354 | C22 | semidirect |
| 10. #17988311 | C22 | semidirect |
| 11. C23×D4×C73 | C4 | semidirect |
| 15. #394×C73 | C4 | semidirect |
| 18. #380×C73 | C4 | semidirect |
| 206. C73 | #11873 | semidirect |
| 207. C23×D4 | Dic73 | semidirect |
| 213. #394 | Dic73 | semidirect |
| 217. #380 | Dic73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22609919 | 2 |
| #22608252 | 2 |
| #22607928 | 2 |
| C73×#2408 | 2 |
| #11873 | 73 |