Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
656 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 218 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#64408 |
| commutator, socle | C22×C73 | C23×C4 |
| Frattini | C22 | C23×#64408 |
| Fitting | #117×C73 | C4 |
| hypercenter | #117 | #64408 |
| hypocenter | C73 | #2296 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #17989538 | C2 | semidirect |
| 5. C4×C4⋊#64408 | C2 | semidirect |
| 18. #14556550 | C4 | semidirect |
| 19. #14556549 | C4 | semidirect |
| 20. #14556548 | C4 | semidirect |
| 21. #14556547 | C4 | semidirect |
| 25. #117×C73 | C4 | semidirect |
| 45. C4⋊Dic73 | C2×C4 | semidirect |
| 46. #11924007 | C2×C4 | semidirect |
| 49. C4×Dic73 | C2×C4 | semidirect |
| 50. C4×Dic73 | C2×C4 | semidirect |
| 52. C4⋊C4×C73 | C2×C4 | semidirect |
| 54. C42×C73 | C2×C4 | semidirect |
| 67. C2×C4×C73 | C4⋊C4 | semidirect |
| 71. C2×Dic73 | C4⋊C4 | semidirect |
| 76. C4×D73 | C4⋊C4 | semidirect |
| 77. C4×D73 | C4⋊C4 | semidirect |
| 107. C73 | #2296 | semidirect |
| 121. #117 | #64408 | semidirect |
| 151. C4⋊C4 | C2×#64408 | semidirect |
| 161. C42 | C2×#64408 | semidirect |
| 185. C2×C4 | C4⋊#64408 | semidirect |