Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
426 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 91 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. C22×#16809951 | C2 | semidirect |
| 3. C2×#20269965 | C2 | semidirect |
| 4. C2×#20269902 | C2 | semidirect |
| 5. C2×#20269899 | C2 | semidirect |
| 6. #27213048 | C2 | semidirect |
| 7. #336×C211 | C2 | semidirect |
| 133. C211 | #2012 | semidirect |
| 141. #336 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16809951 | 2 |
| C22×D1688 | 2 |
| C2×#20269965 | 2 |
| C2×#20269902 | 2 |
| C2×#20269899 | 2 |
| #27213048 | 2 |
| #336×C211 | 2 |
| #2012 | 211 |