Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
820 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 820 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 |
|---|---|---|
| 2. C2×#20269894 | C2 | semidirect |
| 3. C2×#20269893 | C2 | semidirect |
| 4. #27213109 | C2 | semidirect |
| 5. C2×#100×C211 | C2 | semidirect |
| 14. C2×#16809946 | C22 | semidirect |
| 19. C2×M16×C211 | C22 | semidirect |
| 104. C2×D211 | #100 | semidirect |
| 115. C211 | #1783 | semidirect |
| 120. C2×#100 | D211 | semidirect |
| 132. C2×M16 | C2×D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D211 | 2 |
| C2×#20269894 | 2 |
| C2×#20269893 | 2 |
| #27213109 | 2 |
| C2×#100×C211 | 2 |
| #1783 | 211 |