Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D292 |
| commutator | C4×C73 | C23×C4 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | #405×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | #405 | D73 |
| hypocenter | C73 | #2948 |
| LCS | G ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #405 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17989061 | C2 | semidirect |
| 3. #17988700 | C2 | semidirect |
| 4. C4×D584 | C2 | semidirect |
| 5. #17988625 | C2 | semidirect |
| 6. #17988593 | C2 | semidirect |
| 7. #405×C73 | C2 | semidirect |
| 9. C2×D584 | C4 | semidirect |
| 12. C4×D292 | C22 | semidirect |
| 16. #14556525 | C22 | semidirect |
| 17. #14556523 | C22 | semidirect |
| 18. #14556513 | C22 | semidirect |
| 22. #97×C73 | C22 | semidirect |
| 23. C4×C8×C73 | C22 | semidirect |
| 27. C2×D292 | C2×C4 | semidirect |
| 30. D584 | C2×C4 | semidirect |
| 31. D584 | C2×C4 | semidirect |
| 38. C2×C8×C73 | C2×C4 | semidirect |
| 78. C73 | #2948 | semidirect |
| 85. #405 | D73 | semidirect |
| 100. #97 | C2×D73 | semidirect |
| 101. C4×C8 | C2×D73 | semidirect |
| 112. C2×C8 | C4×D73 | semidirect |