Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
432 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 205 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. #27212915 | C2 | direct (N × H) |
| 6. C2×#16809946 | C4 | semidirect |
| 17. #16809946 | C2×C4 | semidirect |
| 77. C2×C211 | #343 | semidirect |
| 81. C211 | C2×#343 | semidirect |
| 159. C2 | #27212915 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16809946 | 2 |
| #27212915 | 2 |
| C22×C4⋊C4×C211 | 2 |
| C2×#343 | 211 |