Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
156 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 50. C211⋊C8 | Q16 | semidirect |
| 72. C211 | #1674 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213549 | 2 |
| #27213357 | 2 |
| #27213353 | 2 |
| #27213270 | 2 |
| #27212898 | 2 |
| #27212891 | 2 |
| #332×C211 | 2 |
| #1674 | 211 |