Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
362 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 1. C2×#20270010 | C2 | semidirect |
| 3. C22×#16809951 | C2 | semidirect |
| 4. C2×#20269895 | C2 | semidirect |
| 5. C2×#20269893 | C2 | semidirect |
| 6. #27213112 | C2 | semidirect |
| 7. #341×C211 | C2 | semidirect |
| 127. C211 | #2019 | semidirect |
| 135. #341 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20270010 | 2 |
| C2×#20270005 | 2 |
| C22×#16809951 | 2 |
| C2×#20269895 | 2 |
| C2×#20269893 | 2 |
| #27213112 | 2 |
| #341×C211 | 2 |
| #2019 | 211 |