Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
586 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 197 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. #22627007 | C2 | semidirect |
| 6. C2×#14556687 | C4 | semidirect |
| 126. C73 | #12551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556687 | 2 |
| #22627007 | 2 |
| C2×#17989551 | 2 |
| #12551 | 73 |