Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
246 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 77 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. #27213199 | C2 | semidirect |
| 3. #27212894 | C2 | semidirect |
| 4. #27212889 | C2 | semidirect |
| 5. #431×C211 | C2 | semidirect |
| 80. C211 | #1543 | semidirect |
| 84. #431 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213696 | 2 |
| #27213199 | 2 |
| #27212894 | 2 |
| #27212889 | 2 |
| #431×C211 | 2 |
| #1543 | 211 |