Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
360 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 3. C2×#20269888 | C2 | semidirect |
| 4. #27212901 | C2 | semidirect |
| 7. C22×C211⋊C8 | C4 | semidirect |
| 11. C22⋊(C211⋊C8) | C4 | semidirect |
| 38. C211⋊C8 | C22⋊C4 | semidirect |
| 59. C22×C211 | #97 | semidirect |
| 74. C211 | #1752 | semidirect |
| 134. C22 | #20269888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C211⋊C8 | 2 |
| C2×C22⋊(C211⋊C8) | 2 |
| C2×#20269888 | 2 |
| #27212901 | 2 |
| C4×C22⋊C4×C211 | 2 |
| #1752 | 211 |