Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
268 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 3. #22624952 | C2 | semidirect |
| 4. #22624940 | C2 | semidirect |
| 128. C73 | #11990 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626304 | 2 |
| #22626274 | 2 |
| #22624952 | 2 |
| #22624940 | 2 |
| #22620584 | 2 |
| #11990 | 73 |