Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
396 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×C22⋊(C211⋊C8) | C2 | semidirect |
| 3. C2×C4×C211⋊C8 | C2 | semidirect |
| 21. C2×C211⋊C8 | D4 | semidirect |
| 25. C2×D4×C211 | C8 | semidirect |
| 73. C4×C211 | C22⋊C8 | semidirect |
| 83. C211 | #1954 | semidirect |
| 104. C2×D4 | C211⋊C8 | semidirect |
| 157. C4 | C22⋊(C211⋊C8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C211⋊C8) | 2 |
| C2×C22⋊(C211⋊C8) | 2 |
| C2×C4×C211⋊C8 | 2 |
| C2×C4×D4×C211 | 2 |
| #1954 | 211 |