Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
300 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#20269913 | C2 | semidirect |
| 3. C2×#20269905 | C2 | semidirect |
| 4. #27213112 | C2 | semidirect |
| 5. C2×C4×C8×C211 | C2 | semidirect |
| 9. C2×Dic844 | C4 | semidirect |
| 10. C2×#16809951 | C4 | semidirect |
| 11. C2×D1688 | C4 | semidirect |
| 85. C211 | #1974 | semidirect |
| 91. C2×C4×C8 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269999 | 2 |
| C2×#20269913 | 2 |
| C2×#20269905 | 2 |
| #27213112 | 2 |
| C2×C4×C8×C211 | 2 |
| #1974 | 211 |