Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
240 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22611982 | C2 | semidirect |
| 4. #22608737 | C2 | semidirect |
| 5. #22608000 | C2 | semidirect |
| 6. #22607979 | C2 | semidirect |
| 120. C73 | #12429 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611982 | 2 |
| #22611968 | 2 |
| #22609536 | 2 |
| #22608737 | 2 |
| #22608000 | 2 |
| #22607979 | 2 |
| C73×#1361 | 2 |
| #12429 | 73 |