Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
474 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 99 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×#20269899 | C2 | semidirect |
| 4. #27213052 | C2 | semidirect |
| 5. #336×C211 | C2 | semidirect |
| 22. C2×Dic422 | D4 | semidirect |
| 40. C2×C8×C211 | D4 | semidirect |
| 62. C2×C4×C211 | SD16 | semidirect |
| 89. C211 | #2014 | semidirect |
| 95. #336 | D211 | semidirect |
| 129. C2×C8 | D844 | semidirect |
| 152. C2×C4 | #16809951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16809951 | 2 |
| C2×#20269974 | 2 |
| C2×#20269899 | 2 |
| #27213052 | 2 |
| #336×C211 | 2 |
| #2014 | 211 |