Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
110 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C211 | D4 |
| commutator | C4 | C2×C16×C211 |
| Frattini, cosocle | C4×C8 | C22×C211 |
| socle | C22×C211 | C22⋊C8 |
| prime radical | C2×D4×C211 | C8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C211 ◁ C4×C8×C211 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4⋊C16×C211 | C2 | semidirect |
| 3. C4×C16×C211 | C2 | semidirect |
| 25. D4×C211 | C16 | semidirect |
| 50. C211 | D4⋊C16 | direct (N × H) |
| 51. D4⋊C16 | C211 | direct (N × H) |
| 53. C4⋊C16 | C2×C211 | semidirect |
| 54. C4×C16 | C2×C211 | semidirect |
| 76. D4 | C16×C211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×D4×C211 | 2 |
| C4⋊C16×C211 | 2 |
| C4×C16×C211 | 2 |
| D4⋊C16 | 211 |