Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
740 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 170 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#64408 |
| commutator, socle | C22×C73 | C23×C4 |
| Fitting | #127×C73 | C4 |
| hypercenter | #127 | #64408 |
| hypocenter | C73 | #2328 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D4×#64408 | C2 | semidirect |
| 2. #17989539 | C2 | semidirect |
| 3. #17989535 | C2 | semidirect |
| 4. #17989531 | C2 | semidirect |
| 5. #17989523 | C2 | semidirect |
| 18. #14556588 | C4 | semidirect |
| 19. #14556587 | C4 | semidirect |
| 20. #14556587 | C4 | semidirect |
| 22. #127×C73 | C4 | semidirect |
| 32. C4×#64408 | D4 | semidirect |
| 34. C2×D292 | C2×C4 | semidirect |
| 35. C2×D292 | C2×C4 | semidirect |
| 36. C2×C22⋊D73 | C2×C4 | semidirect |
| 37. C2×C22⋊D73 | C2×C4 | semidirect |
| 43. C4×Dic73 | C2×C4 | semidirect |
| 44. C4×Dic73 | C2×C4 | semidirect |
| 45. C2×D4×C73 | C2×C4 | semidirect |
| 46. C2×D4×C73 | C2×C4 | semidirect |
| 47. C42×C73 | C2×C4 | semidirect |
| 100. C73 | #2328 | semidirect |
| 113. #127 | #64408 | semidirect |
| 131. C2×D4 | C2×#64408 | semidirect |
| 132. C2×D4 | C2×#64408 | semidirect |
| 147. C42 | C2×#64408 | semidirect |