Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
368 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. C2×#20269910 | C2 | semidirect |
| 3. C2×#20269899 | C2 | semidirect |
| 4. C2×#20269897 | C2 | semidirect |
| 5. C2×(C2×D211)⋊C8 | C2 | semidirect |
| 6. #27213003 | C2 | semidirect |
| 7. #340×C211 | C2 | semidirect |
| 46. C2×C211⋊C8 | D4 | semidirect |
| 143. C211 | #2033 | semidirect |
| 151. #340 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269952 | 2 |
| C2×#20269910 | 2 |
| C2×#20269899 | 2 |
| C2×#20269897 | 2 |
| C2×(C2×D211)⋊C8 | 2 |
| #27213003 | 2 |
| #340×C211 | 2 |
| #2033 | 211 |