Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
242 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 61 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. #27213523 | C2 | semidirect |
| 2. #27213522 | C2 | semidirect |
| 3. #27213522 | C2 | semidirect |
| 4. #27213520 | C2 | semidirect |
| 5. #27213494 | C2 | semidirect |
| 6. #27212868 | C2 | semidirect |
| 7. #486×C211 | C2 | semidirect |
| 50. C211⋊C8 | D8 | semidirect |
| 81. C211 | #1721 | semidirect |
| 88. #486 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213523 | 2 |
| #27213522 | 2 |
| #27213520 | 2 |
| #27213494 | 2 |
| #27212868 | 2 |
| #486×C211 | 2 |
| #1721 | 211 |