Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 69 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×#20269913 | C2 | semidirect |
| 3. #27213147 | C2 | semidirect |
| 4. C2×#20269899 | C2 | semidirect |
| 5. C2×#20269893 | C2 | semidirect |
| 6. #27212914 | C2 | semidirect |
| 7. #408×C211 | C2 | semidirect |
| 116. C211 | #2051 | semidirect |
| 123. #408 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20270002 | 2 |
| C2×#20269913 | 2 |
| #27213147 | 2 |
| C2×#20269899 | 2 |
| C2×#20269893 | 2 |
| #27212914 | 2 |
| #408×C211 | 2 |
| #2051 | 211 |