Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
144 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 69. C211 | #1684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213496 | 2 |
| #27213442 | 2 |
| #27213428 | 2 |
| #27213270 | 2 |
| #27212898 | 2 |
| #27212894 | 2 |
| #332×C211 | 2 |
| #1684 | 211 |