Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
300 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 93 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. #27212909 | C2 | semidirect |
| 5. #27212908 | C2 | semidirect |
| 6. #27212908 | C2 | semidirect |
| 7. #340×C211 | C2 | semidirect |
| 11. #20269935 | C4 | semidirect |
| 118. C211 | #1825 | semidirect |
| 126. #340 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269935 | 2 |
| C2×(C2×D211)⋊C8 | 2 |
| #27213003 | 2 |
| #27212909 | 2 |
| #27212908 | 2 |
| #340×C211 | 2 |
| #1825 | 211 |