Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 2. C2×#20269901 | C2 | semidirect |
| 4. #27212908 | C2 | semidirect |
| 16. C22⋊Q8×C211 | C4 | semidirect |
| 75. C22×C211 | #103 | semidirect |
| 94. C211 | #1892 | semidirect |
| 107. C22⋊Q8 | Dic211 | semidirect |
| 170. C22 | #20269901 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C211⋊C8 | 2 |
| C2×#20269901 | 2 |
| #27213006 | 2 |
| #27212908 | 2 |
| C2×C22⋊Q8×C211 | 2 |
| #1892 | 211 |