Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
480 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 221 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. #27212901 | C2 | semidirect |
| 6. C2×#16809946 | C4 | semidirect |
| 16. C2×C211⋊C8 | C2×C4 | semidirect |
| 43. C2×C4×C211 | M16 | semidirect |
| 65. C211 | #1728 | semidirect |
| 108. 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 |
| #27212901 | 2 |
| C22×C42×C211 | 2 |
| #1728 | 211 |