Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
240 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 10. #20269909 | C4 | semidirect |
| 52. C8×C211 | C4⋊C4 | semidirect |
| 71. C211 | #1944 | semidirect |
| 124. C8 | Dic211⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269911 | 2 |
| C2×#20269909 | 2 |
| #27213044 | 2 |
| #27212909 | 2 |
| C2×#97×C211 | 2 |
| #1944 | 211 |