Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
336 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 93 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×#20269905 | C2 | semidirect |
| 3. C4×#16809946 | C2 | semidirect |
| 4. C4×C4⋊C4×C211 | C2 | semidirect |
| 7. #20269977 | C4 | semidirect |
| 8. #20269974 | C4 | semidirect |
| 9. #20269965 | C4 | semidirect |
| 30. #16809946 | D4 | semidirect |
| 82. C4×C211 | #104 | semidirect |
| 92. C211 | #1980 | semidirect |
| 97. C4×C4⋊C4 | D211 | semidirect |
| 176. C4 | #20269905 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213696 | 2 |
| C2×#20269905 | 2 |
| C4×#16809946 | 2 |
| C4×C4⋊C4×C211 | 2 |
| #1980 | 211 |