Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
230 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 230 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. #27213172 | C2 | semidirect |
| 5. #27212911 | C2 | semidirect |
| 6. #27212906 | C2 | semidirect |
| 7. C2×C4×C8×C211 | C2 | semidirect |
| 14. #20269902 | C4 | semidirect |
| 15. #20269899 | C4 | semidirect |
| 90. C211 | #1937 | semidirect |
| 96. C2×C4×C8 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213172 | 2 |
| C2×#20269905 | 2 |
| #27213143 | 2 |
| #27213112 | 2 |
| #27212911 | 2 |
| #27212906 | 2 |
| C2×C4×C8×C211 | 2 |
| #1937 | 211 |