Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
396 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×C4⋊(C211⋊C8) | C2 | semidirect |
| 3. C2×(C2×D211)⋊C8 | C2 | semidirect |
| 4. C2×C4×C8×C211 | C2 | semidirect |
| 20. C2×D844 | C8 | semidirect |
| 35. C2×C8×C211 | D4 | semidirect |
| 72. C4×C211 | C22⋊C8 | semidirect |
| 83. C211 | #1954 | semidirect |
| 88. C2×C4×C8 | D211 | semidirect |
| 117. C2×C8 | D844 | semidirect |
| 157. C4 | (C2×D211)⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D844 | 2 |
| C2×C4⋊(C211⋊C8) | 2 |
| C2×(C2×D211)⋊C8 | 2 |
| C2×C4×C8×C211 | 2 |
| #1954 | 211 |