Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1220 conjugacy classes of subgroups; only the 220 normal subgroups are shown.
This group has 1220 conjugacy classes of subgroups — too many to draw. Only its 220 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. #22626533 | C2 | semidirect |
| 2. #22626210 | C2 | semidirect |
| 3. #22626202 | C2 | semidirect |
| 7. #17989566 | C22 | semidirect |
| 8. #17989493 | C22 | semidirect |
| 9. #17989491 | C22 | semidirect |
| 13. #17989158 | C4 | semidirect |
| 16. C2×#14556578 | C4 | semidirect |
| 17. #41×Dic73 | C4 | semidirect |
| 18. C2×H(5,𝔽2)×C73 | C4 | semidirect |
| 142. C73 | #33362 | semidirect |
| 144. C2×H(5,𝔽2) | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626533 | 2 |
| #22626210 | 2 |
| #22626202 | 2 |
| #22623719 | 2 |
| #33362 | 73 |