Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 1. C22×C4⋊Dic211 | C2 | semidirect |
| 2. C2×#20269898 | C2 | semidirect |
| 3. C2×C22⋊(C211⋊C8) | C2 | semidirect |
| 4. #27212908 | C2 | semidirect |
| 17. #121×C211 | C4 | semidirect |
| 29. C4⋊Dic211 | D4 | semidirect |
| 38. C2×D4×C211 | C2×C4 | semidirect |
| 47. C4⋊C4×C211 | C2×C4 | semidirect |
| 97. C22×C211 | #102 | semidirect |
| 119. C211 | #1874 | semidirect |
| 132. #121 | Dic211 | semidirect |
| 148. C2×D4 | C2×Dic211 | semidirect |
| 167. C4⋊C4 | C2×Dic211 | semidirect |
| 217. C22 | #20269898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic211 | 2 |
| C2×#20269898 | 2 |
| C2×C22⋊(C211⋊C8) | 2 |
| #27212908 | 2 |
| C2×#121×C211 | 2 |
| #1874 | 211 |