Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
308 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 11. #20269942 | C4 | semidirect |
| 58. Dic422 | C4⋊C4 | semidirect |
| 102. Dic211 | #103 | semidirect |
| 110. C211 | #1803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269942 | 2 |
| C2×Dic211⋊C8 | 2 |
| C2×#20269902 | 2 |
| C2×#20269900 | 2 |
| #27213015 | 2 |
| #27212908 | 2 |
| #340×C211 | 2 |
| #1803 | 211 |