Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
516 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#64408 |
| commutator, socle | C22×C73 | C23×C4 |
| Fitting | #126×C73 | C4 |
| hypercenter | #126 | #64408 |
| hypocenter | C73 | C4×#126 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17989536 | C2 | semidirect |
| 3. #17989532 | C2 | semidirect |
| 4. C4⋊C4×#64408 | C2 | semidirect |
| 6. C42×#64408 | C2 | semidirect |
| 18. #14556586 | C4 | semidirect |
| 19. #14556585 | C4 | semidirect |
| 20. #14556584 | C4 | semidirect |
| 24. #126×C73 | C4 | semidirect |
| 38. C4⋊Dic73 | C2×C4 | semidirect |
| 39. #11924007 | C2×C4 | semidirect |
| 40. #11924007 | C2×C4 | semidirect |
| 44. C4×Dic73 | C2×C4 | semidirect |
| 45. C4⋊C4×C73 | C2×C4 | semidirect |
| 47. C42×C73 | C2×C4 | semidirect |
| 80. #64408 | #126 | direct (N × H) |
| 91. C73 | C4×#126 | semidirect |
| 103. #126 | #64408 | direct (N × H) |
| 128. C4⋊C4 | C2×#64408 | semidirect |
| 138. C42 | C2×#64408 | semidirect |