Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
166 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 166 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 |
|---|---|---|
| 4. #27212897 | C2 | semidirect |
| 5. #27212892 | C2 | semidirect |
| 6. #27212892 | C2 | semidirect |
| 7. #487×C211 | C2 | semidirect |
| 77. C211 | #1679 | semidirect |
| 79. #487 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213423 | 2 |
| #27213348 | 2 |
| C8×D844 | 2 |
| #27212897 | 2 |
| #27212892 | 2 |
| #487×C211 | 2 |
| #1679 | 211 |