Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
272 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 272 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 |
|---|---|---|
| 4. #27212918 | C2 | semidirect |
| 5. #27212917 | C2 | semidirect |
| 6. #27212916 | C2 | semidirect |
| 7. #344×C211 | C2 | semidirect |
| 89. C211 | #1829 | semidirect |
| 97. #344 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213620 | 2 |
| C2×#20269893 | 2 |
| #27212918 | 2 |
| #27212917 | 2 |
| #27212916 | 2 |
| #344×C211 | 2 |
| #1829 | 211 |