Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
256 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 256 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 |
|---|---|---|
| 16. C4⋊C8×C211 | C4 | semidirect |
| 68. C4×C211 | #107 | semidirect |
| 83. C211 | #1947 | semidirect |
| 99. C4⋊C8 | Dic211 | semidirect |
| 155. C4 | #20269911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269911 | 2 |
| #27213016 | 2 |
| C4×C4⋊Dic211 | 2 |
| #27212909 | 2 |
| C2×C4⋊C8×C211 | 2 |
| #1947 | 211 |