Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
308 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 308 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 |
|---|---|---|
| 10. Q8×Dic211 | C4 | semidirect |
| 72. Q8×C211 | C4⋊C4 | semidirect |
| 102. Dic211 | #103 | semidirect |
| 110. C211 | #1803 | semidirect |
| 170. Q8 | Dic211⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic211 | 2 |
| C2×Dic211⋊C8 | 2 |
| C2×#20269901 | 2 |
| #27213015 | 2 |
| #27212909 | 2 |
| #27212908 | 2 |
| C2×#103×C211 | 2 |
| #1803 | 211 |