Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 256 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 |
|---|---|---|
| 16. #20269887 | C4 | semidirect |
| 52. C211⋊C8 | C4⋊C4 | semidirect |
| 64. C8×C211 | C4⋊C4 | semidirect |
| 84. C211 | #1847 | semidirect |
| 149. C8 | Dic211⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269910 | 2 |
| C2×#20269909 | 2 |
| C2×#20269908 | 2 |
| C2×#20269887 | 2 |
| #27213015 | 2 |
| #27213011 | 2 |
| C2×#107×C211 | 2 |
| #1847 | 211 |