Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
422 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 161 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×C4 | C23×D73 |
| commutator, socle | C22×C73 | C23×C4 |
| Fitting | #433×C73 | C2 |
| hypercenter | #433 | D73 |
| hypocenter | C73 | #2977 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ #433 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17988660 | C2 | semidirect |
| 3. #17988657 | C2 | semidirect |
| 4. C8×D292 | C2 | semidirect |
| 5. #17988652 | C2 | semidirect |
| 6. #17988648 | C2 | semidirect |
| 7. #17988552 | C2 | semidirect |
| 8. C22⋊C8×D73 | C2 | semidirect |
| 9. #433×C73 | C2 | semidirect |
| 12. C2×#11924011 | C22 | semidirect |
| 15. C2×C8×D73 | C22 | semidirect |
| 22. C4⋊#10596831 | C22 | semidirect |
| 26. #14556503 | C22 | semidirect |
| 27. #14556503 | C22 | semidirect |
| 28. #14556502 | C22 | semidirect |
| 29. C4×#10596831 | C22 | semidirect |
| 31. C4⋊C8×C73 | C22 | semidirect |
| 33. #97×C73 | C22 | semidirect |
| 34. C4×C8×C73 | C22 | semidirect |
| 115. C73 | #2977 | semidirect |
| 122. #433 | D73 | semidirect |
| 139. C4⋊C8 | C2×D73 | semidirect |
| 147. #97 | C2×D73 | semidirect |
| 149. C4×C8 | C2×D73 | semidirect |