Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
480 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 234 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C2×C32 | C22×C33 |
| prime radical | C33×D4 | C32 |
| LCS | G ▷ C2×C32 ▷ C1 | |
| UCS | C1 ◁ C2×C32 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#6896 | C2 | semidirect |
| 2. C4×#6896 | C2 | semidirect |
| 4. D4×C9⋊C9 | C3 | semidirect |
| 5. D4×C9⋊C9 | C3 | semidirect |
| 7. D4×C92 | C3 | semidirect |
| 12. C22×C9⋊C9 | C2×C3 | semidirect |
| 13. C22×C9⋊C9 | C2×C3 | semidirect |
| 15. C22×C92 | C2×C3 | semidirect |
| 16. C4×C9⋊C9 | C2×C3 | semidirect |
| 17. C4×C9⋊C9 | C2×C3 | semidirect |
| 19. C4×C92 | C2×C3 | semidirect |
| 20. #6896 | D4 | direct (N × H) |
| 50. C9⋊C9 | C3×D4 | semidirect |
| 51. C9⋊C9 | C3×D4 | semidirect |
| 53. C92 | C3×D4 | semidirect |
| 60. D4×C9 | 3−1+2 | semidirect |
| 82. C22×C9 | C2×3−1+2 | semidirect |
| 86. C4×C9 | C2×3−1+2 | semidirect |
| 122. C9 | D4×3−1+2 | semidirect |
| 123. D4 | #6896 | direct (N × H) |
| 130. C22 | C2×#6896 | semidirect |
| 131. C4 | C2×#6896 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6896 | 2 |
| C4×#6896 | 2 |
| C3×D4×3−1+2 | 3 |
| D4×C9⋊C9 | 3 |
| D4×C32⋊C9 | 3 |
| D4×C92 | 3 |