Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
340 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 89 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. #27213006 | C2 | semidirect |
| 3. #27212881 | C2 | semidirect |
| 4. C2×C22⋊C8×C211 | C2 | semidirect |
| 5. C22×D844 | C4 | semidirect |
| 9. #20269951 | C4 | semidirect |
| 12. C2×C4⋊Dic211 | C4 | semidirect |
| 15. C211⋊#95 | C22 | semidirect |
| 19. C22⋊C8×C211 | C22 | semidirect |
| 109. C211 | #1519 | semidirect |
| 112. C2×C22⋊C8 | D211 | semidirect |
| 128. C22⋊C8 | C2×D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269951 | 2 |
| #27213006 | 2 |
| #27212881 | 2 |
| C2×C22⋊C8×C211 | 2 |
| #1519 | 211 |