Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
224 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 77 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. C2×#20269912 | C2 | semidirect |
| 5. #27212905 | C2 | semidirect |
| 6. #27212900 | C2 | semidirect |
| 7. #405×C211 | C2 | semidirect |
| 14. #20269900 | C4 | semidirect |
| 15. #20269900 | C4 | semidirect |
| 16. #20269897 | C4 | semidirect |
| 17. #20269897 | C4 | semidirect |
| 105. C211 | #1929 | semidirect |
| 111. #405 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269912 | 2 |
| C2×#20269903 | 2 |
| #27213140 | 2 |
| #27213112 | 2 |
| #27212905 | 2 |
| #27212900 | 2 |
| #405×C211 | 2 |
| #1929 | 211 |