Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
332 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 83 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×#20269983 | C2 | semidirect |
| 3. #27213148 | C2 | semidirect |
| 4. C2×#20269899 | C2 | semidirect |
| 5. C2×#20269893 | C2 | semidirect |
| 6. #27212914 | C2 | semidirect |
| 7. #341×C211 | C2 | semidirect |
| 11. #20270005 | C4 | semidirect |
| 123. C211 | #1907 | semidirect |
| 131. #341 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20270005 | 2 |
| C2×#20269983 | 2 |
| #27213148 | 2 |
| C2×#20269899 | 2 |
| C2×#20269893 | 2 |
| #27212914 | 2 |
| #341×C211 | 2 |
| #1907 | 211 |