Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
172 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 172 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 |
|---|---|---|
| 1. #27213549 | C2 | semidirect |
| 5. #27212898 | C2 | semidirect |
| 6. #27212891 | C2 | semidirect |
| 7. #332×C211 | C2 | semidirect |
| 53. C211⋊C8 | SD16 | semidirect |
| 78. C211 | #1673 | semidirect |
| 86. #332 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213549 | 2 |
| #27213352 | 2 |
| #27213348 | 2 |
| #27213211 | 2 |
| #27212898 | 2 |
| #27212891 | 2 |
| #332×C211 | 2 |
| #1673 | 211 |