Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
274 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 63 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. #27213194 | C2 | semidirect |
| 3. #27213163 | C2 | semidirect |
| 4. #27213152 | C2 | semidirect |
| 5. C2×#20269893 | C2 | semidirect |
| 6. #27212917 | C2 | semidirect |
| 7. #413×C211 | C2 | semidirect |
| 110. C211 | #2048 | semidirect |
| 116. #413 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20270002 | 2 |
| #27213194 | 2 |
| #27213163 | 2 |
| #27213152 | 2 |
| C2×#20269893 | 2 |
| #27212917 | 2 |
| #413×C211 | 2 |
| #2048 | 211 |