Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
456 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×#10596842 |
| commutator, socle | C2×C73 | C23×C8 |
| Frattini | C2 | C23×#10596842 |
| Fitting | #41×C73 | C8 |
| hypercenter | #41 | #10596842 |
| hypocenter | C73 | C8×#41 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C4 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×#10596842 | C2 | semidirect |
| 2. D4×#10596842 | C2 | semidirect |
| 3. #17989700 | C2 | semidirect |
| 4. C2×C4×#10596842 | C2 | semidirect |
| 31. #11924029 | C8 | semidirect |
| 32. #11924028 | C8 | semidirect |
| 33. #11924027 | C8 | semidirect |
| 37. #41×C73 | C8 | semidirect |
| 46. #10596842 | #41 | direct (N × H) |
| 47. Q8×C73 | C2×C8 | semidirect |
| 48. D4×C73 | C2×C8 | semidirect |
| 49. C2×C4×C73 | C2×C8 | semidirect |
| 50. C22⋊D73 | C2×C8 | semidirect |
| 51. C2×Dic73 | C2×C8 | semidirect |
| 52. D292 | C2×C8 | semidirect |
| 53. C4×D73 | C2×C8 | semidirect |
| 54. C4×D73 | C2×C8 | semidirect |
| 57. Dic146 | C2×C8 | semidirect |
| 77. C73 | C8×#41 | semidirect |
| 99. #41 | #10596842 | direct (N × H) |
| 117. Q8 | C2×#10596842 | semidirect |
| 120. D4 | C2×#10596842 | semidirect |
| 132. C2×C4 | C2×#10596842 | semidirect |