Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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×#20269911 | C2 | semidirect |
| 4. #27213045 | C2 | semidirect |
| 5. #27212908 | C2 | semidirect |
| 6. #27212900 | C2 | semidirect |
| 23. #102×C211 | C4 | semidirect |
| 53. C2×C8×C211 | C2×C4 | semidirect |
| 55. C4⋊C4×C211 | C2×C4 | semidirect |
| 81. D4×C211 | C4⋊C4 | semidirect |
| 123. C211 | #1862 | semidirect |
| 146. #102 | Dic211 | semidirect |
| 169. C2×C8 | C2×Dic211 | semidirect |
| 176. C4⋊C4 | C2×Dic211 | semidirect |
| 191. D4 | C4⋊Dic211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic211 | 2 |
| C2×#20269911 | 2 |
| C2×#20269898 | 2 |
| #27213045 | 2 |
| #27212908 | 2 |
| #27212900 | 2 |
| C2×#102×C211 | 2 |
| #1862 | 211 |