Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
474 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×#17988380 | C2 | semidirect |
| 3. #22608095 | C2 | semidirect |
| 4. #22608093 | C2 | semidirect |
| 5. C2×#353×C73 | C2 | semidirect |
| 8. #17989137 | C4 | semidirect |
| 11. #17988963 | C4 | semidirect |
| 13. #17988959 | C4 | semidirect |
| 16. C4×#11924012 | C4 | semidirect |
| 37. #14556591 | C2×C4 | semidirect |
| 38. #14556588 | C2×C4 | semidirect |
| 46. C4×#10596831 | C2×C4 | semidirect |
| 47. C4×#10596831 | C2×C4 | semidirect |
| 193. C2×#353 | D73 | semidirect |
| 196. C73 | #13584 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620381 | 2 |
| C2×#17988380 | 2 |
| #22608095 | 2 |
| #22608093 | 2 |
| C2×#353×C73 | 2 |
| #13584 | 73 |