Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
424 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 3. #27212909 | C2 | semidirect |
| 4. #27212908 | C2 | semidirect |
| 5. #340×C211 | C2 | semidirect |
| 9. C2×C8×D211 | C4 | semidirect |
| 11. #20269935 | C4 | semidirect |
| 82. C211 | #1735 | semidirect |
| 88. #340 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D211 | 2 |
| C2×#20269935 | 2 |
| #27212909 | 2 |
| #27212908 | 2 |
| #340×C211 | 2 |
| #1735 | 211 |