Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
348 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 107 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×#20269908 | C2 | semidirect |
| 3. C2×#20269900 | C2 | semidirect |
| 5. C2×C4×C211⋊C8 | C2 | semidirect |
| 6. #27213052 | C2 | semidirect |
| 11. C2×#16809950 | C4 | semidirect |
| 66. C211⋊C8 | C22⋊C4 | semidirect |
| 81. C2×C4×C211 | SD16 | semidirect |
| 112. C211 | #1968 | semidirect |
| 192. C2×C4 | #16809950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16809950 | 2 |
| C2×#20269908 | 2 |
| C2×#20269900 | 2 |
| C2×#20269898 | 2 |
| C2×C4×C211⋊C8 | 2 |
| #27213052 | 2 |
| #390×C211 | 2 |
| #1968 | 211 |