Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
432 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 432 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 | #41×C73 | C8 |
| hypercenter | #41 | #10596842 |
| hypocenter | C73 | #2988 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ #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 |
| 48. Q8×C73 | C2×C8 | semidirect |
| 49. D4×C73 | C2×C8 | semidirect |
| 50. C2×C4×C73 | C2×C8 | semidirect |
| 51. C22⋊D73 | C2×C8 | semidirect |
| 52. C2×Dic73 | C2×C8 | semidirect |
| 53. D292 | C2×C8 | semidirect |
| 54. C4×D73 | C2×C8 | semidirect |
| 55. C4×D73 | C2×C8 | semidirect |
| 58. Dic146 | C2×C8 | semidirect |
| 79. C73 | #2988 | semidirect |
| 101. #41 | #10596842 | semidirect |
| 119. Q8 | C2×#10596842 | semidirect |
| 122. D4 | C2×#10596842 | semidirect |
| 135. C2×C4 | C2×#10596842 | semidirect |