Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
256 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#20269913 | C2 | semidirect |
| 2. #27213184 | C2 | semidirect |
| 4. #27212918 | C2 | semidirect |
| 16. #131×C211 | C4 | semidirect |
| 17. #131×C211 | C4 | semidirect |
| 91. C211 | #1814 | semidirect |
| 101. #131 | Dic211 | semidirect |
| 102. #131 | Dic211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269913 | 2 |
| #27213184 | 2 |
| #27213163 | 2 |
| #27212918 | 2 |
| C2×#131×C211 | 2 |
| #1814 | 211 |