Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
348 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 3. C2×#20269888 | C2 | semidirect |
| 4. C2×C4×C211⋊C8 | C2 | semidirect |
| 5. #27212901 | C2 | semidirect |
| 6. #27212901 | C2 | semidirect |
| 10. C2×#16809946 | C4 | semidirect |
| 15. C22⋊(C211⋊C8) | C4 | semidirect |
| 55. C211⋊C8 | C22⋊C4 | semidirect |
| 74. C2×C4×C211 | M16 | semidirect |
| 104. C211 | #1753 | semidirect |
| 175. C2×C4 | #16809946 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16809946 | 2 |
| C2×C22⋊(C211⋊C8) | 2 |
| C2×#20269888 | 2 |
| C2×C4×C211⋊C8 | 2 |
| #27212901 | 2 |
| C4×C22⋊C4×C211 | 2 |
| #1753 | 211 |