Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
236 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 83. C211 | #1830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213623 | 2 |
| C2×#20269895 | 2 |
| #27212918 | 2 |
| #27212917 | 2 |
| #27212916 | 2 |
| #344×C211 | 2 |
| #1830 | 211 |