Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. C2×C4⋊(C211⋊C8) | C2 | semidirect |
| 2. #27212890 | C2 | direct (N × H) |
| 6. C4⋊(C211⋊C8) | C22 | semidirect |
| 57. C2×C211 | #331 | semidirect |
| 60. C211 | C2×#331 | semidirect |
| 118. C2 | #27212890 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C211⋊C8) | 2 |
| #27212890 | 2 |
| C2×#127×C211 | 2 |
| C2×#331 | 211 |