Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
760 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 407 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #10596842 |
| commutator, hypocenter | C73 | C22×C4×C8 |
| Frattini | C2 | C23×#10596842 |
| Fitting | C22×C4×C73 | C8 |
| socle | C23×C73 | C2×C8 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×#10596842 | C2 | direct (N × H) |
| 4. C22×#10596842 | C4 | direct (N × H) |
| 6. C4×#10596842 | C22 | direct (N × H) |
| 12. C2×#10596842 | C2×C4 | direct (N × H) |
| 14. C22×#64408 | C8 | semidirect |
| 22. C22×Dic73 | C8 | semidirect |
| 23. C2×C4×D73 | C8 | semidirect |
| 25. C22×C4×C73 | C8 | semidirect |
| 32. C2×#64408 | C2×C8 | semidirect |
| 37. #10596842 | C22×C4 | direct (N × H) |
| 38. C2×C4×C73 | C2×C8 | semidirect |
| 39. C2×Dic73 | C2×C8 | semidirect |
| 40. C4×D73 | C2×C8 | semidirect |
| 42. C22×C73 | C4×C8 | semidirect |
| 44. C2×D73 | C4×C8 | semidirect |
| 50. #64408 | C22×C8 | semidirect |
| 52. C4×C73 | C22×C8 | semidirect |
| 53. Dic73 | C22×C8 | semidirect |
| 54. C2×C73 | C2×C4×C8 | semidirect |
| 56. D73 | C2×C4×C8 | semidirect |
| 60. C73 | C22×C4×C8 | semidirect |
| 81. C22×C4 | #10596842 | direct (N × H) |
| 100. C2×C4 | C2×#10596842 | direct (N × H) |
| 107. C22 | C4×#10596842 | direct (N × H) |
| 113. C4 | C22×#10596842 | direct (N × H) |
| 117. C2 | C2×C4×#10596842 | direct (N × H) |