Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
180 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #27212899 | C2 | semidirect |
| 4. #27212897 | C2 | semidirect |
| 26. M16×C211 | C8 | semidirect |
| 49. C8×C211 | C2×C8 | semidirect |
| 66. C211 | #1565 | semidirect |
| 89. M16 | C211⋊C8 | semidirect |
| 116. C8 | C2×C211⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213199 | 2 |
| C2×C4⋊(C211⋊C8) | 2 |
| #27212899 | 2 |
| #27212897 | 2 |
| C4×M16×C211 | 2 |
| #1565 | 211 |