Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
224 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 9. #20269911 | C4 | semidirect |
| 10. #20269909 | C4 | semidirect |
| 12. #20269887 | C4 | semidirect |
| 16. #108×C211 | C4 | semidirect |
| 62. C211 | #1773 | semidirect |
| 74. #108 | Dic211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213184 | 2 |
| #27213104 | 2 |
| C2×#20269887 | 2 |
| #27212907 | 2 |
| C2×#108×C211 | 2 |
| #1773 | 211 |