Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
500 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 191 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#10596842 |
| commutator, socle | C2×C73 | C23×C8 |
| Fitting | C2×D4×C73 | C8 |
| hypercenter | C2×D4 | #10596842 |
| hypocenter | C73 | #2972 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D4×#10596842 | C2 | semidirect |
| 2. #17989700 | C2 | semidirect |
| 3. C2×C22⋊#10596842 | C2 | semidirect |
| 5. C22×#10596842 | C22 | semidirect |
| 6. C4⋊#10596842 | C22 | semidirect |
| 8. C22⋊#10596842 | C22 | semidirect |
| 9. C4×#10596842 | C22 | semidirect |
| 30. C2×D292 | C8 | semidirect |
| 31. C2×C22⋊D73 | C8 | semidirect |
| 32. D4×D73 | C8 | semidirect |
| 35. C2×D4×C73 | C8 | semidirect |
| 36. C23×C73 | C2×C8 | semidirect |
| 39. C22×D73 | C2×C8 | semidirect |
| 40. C22×D73 | C2×C8 | semidirect |
| 53. D4×C73 | C2×C8 | semidirect |
| 54. C2×C4×C73 | C2×C8 | semidirect |
| 55. C22⋊D73 | C2×C8 | semidirect |
| 56. C2×Dic73 | C2×C8 | semidirect |
| 57. D292 | C2×C8 | semidirect |
| 58. C4×D73 | C2×C8 | semidirect |
| 86. C73 | #2972 | semidirect |
| 108. C2×D4 | #10596842 | semidirect |
| 128. C23 | C2×#10596842 | semidirect |
| 131. D4 | C2×#10596842 | semidirect |
| 144. C2×C4 | C2×#10596842 | semidirect |