Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
360 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 209 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C23×D73 |
| commutator, socle | C2×C73 | C23×C8 |
| Fitting | #504×C73 | C2 |
| hypercenter | #504 | D73 |
| hypocenter | C73 | #3407 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C8 ◁ #504 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17989005 | C2 | semidirect |
| 3. #17989004 | C2 | semidirect |
| 4. #17989003 | C2 | semidirect |
| 5. C2×#14556530 | C2 | semidirect |
| 6. M32×D73 | C2 | semidirect |
| 7. #504×C73 | C2 | semidirect |
| 14. #14556531 | C22 | semidirect |
| 17. #14556530 | C22 | semidirect |
| 18. #14556530 | C22 | semidirect |
| 19. C2×#11924003 | C22 | semidirect |
| 20. C16×D73 | C22 | semidirect |
| 22. M32×C73 | C22 | semidirect |
| 23. C2×C16×C73 | C22 | semidirect |
| 73. C73 | #3407 | semidirect |
| 78. #504 | D73 | semidirect |
| 93. M32 | C2×D73 | semidirect |
| 96. C2×C16 | C2×D73 | semidirect |