Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1188 conjugacy classes of subgroups; only the 220 normal subgroups are shown.
This group has 1188 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. #22626213 | C2 | semidirect |
| 3. #22626202 | C2 | semidirect |
| 14. #17989158 | C4 | semidirect |
| 16. C2×#14556589 | C4 | semidirect |
| 17. #41×Dic73 | C4 | semidirect |
| 18. C2×2−1+4×C73 | C4 | semidirect |
| 140. C73 | #33360 | semidirect |
| 142. C2×2−1+4 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626533 | 2 |
| #22626213 | 2 |
| #22626202 | 2 |
| #22623712 | 2 |
| #33360 | 73 |