Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
390 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 101 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. C22×#16809946 | C2 | semidirect |
| 2. C2×#20269894 | C2 | semidirect |
| 3. #27213110 | C2 | semidirect |
| 4. #27212915 | C2 | semidirect |
| 27. #16809946 | D4 | semidirect |
| 97. C22×C211 | #100 | semidirect |
| 113. C211 | #1900 | semidirect |
| 211. C22 | #20269894 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16809946 | 2 |
| C2×#20269894 | 2 |
| #27213110 | 2 |
| #27212915 | 2 |
| C2×#121×C211 | 2 |
| #1900 | 211 |