Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
220 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 60 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. #22625578 | C2 | semidirect |
| 3. #22624955 | C2 | semidirect |
| 4. #22624891 | C2 | semidirect |
| 6. #22624850 | C2 | semidirect |
| 110. C73 | #12077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625578 | 2 |
| #22625529 | 2 |
| #22624955 | 2 |
| #22624891 | 2 |
| #22624890 | 2 |
| #22624850 | 2 |
| #22611798 | 2 |
| #12077 | 73 |