Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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. C42×Dic211 | C2 | semidirect |
| 4. #27212907 | C2 | semidirect |
| 5. C4×M16×C211 | C2 | semidirect |
| 7. C4×Dic422 | C4 | semidirect |
| 8. C4×D844 | C4 | semidirect |
| 15. #20269903 | C4 | direct (N × H) |
| 36. C4×Dic211 | C2×C4 | semidirect |
| 40. M16×C211 | C2×C4 | semidirect |
| 47. Dic422 | C42 | semidirect |
| 49. D844 | C42 | semidirect |
| 72. C4×C211 | #104 | semidirect |
| 83. C211 | C4×#104 | semidirect |
| 87. C4×M16 | D211 | semidirect |
| 115. M16 | C4×D211 | semidirect |
| 159. C4 | #20269903 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16809962 | 2 |
| C2×#20269903 | 2 |
| C42×Dic211 | 2 |
| #27212907 | 2 |
| C4×M16×C211 | 2 |
| C4×#104 | 211 |