Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
464 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22608272 | C2 | semidirect |
| 3. #22607955 | C2 | semidirect |
| 4. #22607928 | C2 | semidirect |
| 12. C2×#121×C73 | C4 | semidirect |
| 14. #400×C73 | C4 | semidirect |
| 17. #394×C73 | C4 | semidirect |
| 22. #381×C73 | C4 | semidirect |
| 209. C73 | #11824 | semidirect |
| 210. C2×#121 | Dic73 | semidirect |
| 214. #400 | Dic73 | semidirect |
| 217. #394 | Dic73 | semidirect |
| 222. #381 | Dic73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22609919 | 2 |
| #22608272 | 2 |
| #22607955 | 2 |
| #22607928 | 2 |
| C73×#2635 | 2 |
| #11824 | 73 |