Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
532 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 141 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 | C2×C4×C73 | C24 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | #431×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | #431 | D73 |
| hypocenter | C73 | #3205 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #431 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17989137 | C2 | semidirect |
| 2. C2×#14556588 | C2 | semidirect |
| 3. #17988964 | C2 | semidirect |
| 4. #17988934 | C2 | semidirect |
| 5. #17988783 | C2 | semidirect |
| 6. #17988723 | C2 | semidirect |
| 7. #431×C73 | C2 | semidirect |
| 12. C2×D584 | C22 | semidirect |
| 13. #14556591 | C22 | semidirect |
| 18. #14556588 | C22 | semidirect |
| 23. C4×D292 | C22 | semidirect |
| 24. #14556513 | C22 | semidirect |
| 26. C4⋊C8×C73 | C22 | semidirect |
| 28. C4×C8×C73 | C22 | semidirect |
| 67. C2×C4×C73 | D8 | semidirect |
| 113. C73 | #3205 | semidirect |
| 120. #431 | D73 | semidirect |
| 138. C4⋊C8 | C2×D73 | semidirect |
| 141. C4×C8 | C2×D73 | semidirect |
| 193. C2×C4 | D584 | semidirect |