Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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. C4×#16809946 | C2 | semidirect |
| 3. #27212915 | C2 | semidirect |
| 6. #20269894 | C4 | direct (N × H) |
| 17. #16809946 | C2×C4 | semidirect |
| 67. C4×C211 | #100 | semidirect |
| 75. C211 | C4×#100 | semidirect |
| 143. C4 | #20269894 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269894 | 2 |
| C4×#16809946 | 2 |
| #27212915 | 2 |
| C2×C4×D4×C211 | 2 |
| C4×#100 | 211 |