Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
168 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 168 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 |
|---|---|---|
| 2. #27213428 | C2 | semidirect |
| 4. #27213273 | C2 | semidirect |
| 5. #27212898 | C2 | semidirect |
| 7. #332×C211 | C2 | semidirect |
| 54. C211⋊C8 | SD16 | semidirect |
| 79. C211 | #1686 | semidirect |
| 86. #332 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213520 | 2 |
| #27213428 | 2 |
| #27213347 | 2 |
| #27213273 | 2 |
| #27212898 | 2 |
| #27212889 | 2 |
| #332×C211 | 2 |
| #1686 | 211 |