Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
300 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 83 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×#20269912 | C2 | semidirect |
| 3. C2×#20269904 | C2 | semidirect |
| 4. C2×#20269903 | C2 | semidirect |
| 5. #27213112 | C2 | semidirect |
| 6. C2×C8×Dic211 | C2 | semidirect |
| 7. #408×C211 | C2 | semidirect |
| 11. C2×#16809952 | C4 | semidirect |
| 12. C2×#16809950 | C4 | semidirect |
| 13. C2×#16809949 | C4 | semidirect |
| 14. C2×#16809947 | C4 | semidirect |
| 119. C211 | #1974 | semidirect |
| 126. #408 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269997 | 2 |
| C2×#20269912 | 2 |
| C2×#20269904 | 2 |
| C2×#20269903 | 2 |
| #27213112 | 2 |
| C2×C8×Dic211 | 2 |
| #408×C211 | 2 |
| #1974 | 211 |