Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
698 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22610005 | C2 | semidirect |
| 2. C2×#17988311 | C2 | semidirect |
| 3. #22607952 | C2 | semidirect |
| 4. #22607928 | C2 | semidirect |
| 12. C22×#41×C73 | C4 | semidirect |
| 15. #393×C73 | C4 | semidirect |
| 17. #392×C73 | C4 | semidirect |
| 22. #381×C73 | C4 | semidirect |
| 240. C73 | #11839 | semidirect |
| 241. C22×#41 | Dic73 | semidirect |
| 245. #393 | Dic73 | semidirect |
| 247. #392 | Dic73 | semidirect |
| 252. #381 | Dic73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22610005 | 2 |
| C2×#17988311 | 2 |
| #22607952 | 2 |
| #22607928 | 2 |
| C73×#2404 | 2 |
| #11839 | 73 |