Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
368 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 89 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×#20269911 | C2 | semidirect |
| 3. C2×#20269899 | C2 | semidirect |
| 4. C2×#20269899 | C2 | semidirect |
| 5. #27213006 | C2 | semidirect |
| 6. #27212909 | C2 | semidirect |
| 7. C2×C22⋊C8×C211 | C2 | semidirect |
| 60. C2×C8×C211 | D4 | semidirect |
| 143. C211 | #2033 | semidirect |
| 149. C2×C22⋊C8 | D211 | semidirect |
| 196. C2×C8 | C22⋊D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269951 | 2 |
| C2×#20269911 | 2 |
| C2×#20269899 | 2 |
| #27213006 | 2 |
| #27212909 | 2 |
| C2×C22⋊C8×C211 | 2 |
| #2033 | 211 |