Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
316 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×#10596842 |
| commutator | C2×C73 | C2×C4×C8 |
| Frattini | C22 | C22×#10596842 |
| Fitting | C42×C73 | C8 |
| socle | C22×C73 | C22×C8 |
| hypercenter | C42 | #10596842 |
| hypocenter | C73 | C4×C4⋊C8 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C4⋊#10596842 | C4 | direct (N × H) |
| 25. C4×#64408 | C8 | semidirect |
| 32. C4×Dic73 | C8 | semidirect |
| 33. C4×Dic73 | C8 | semidirect |
| 34. C4×Dic73 | C8 | semidirect |
| 35. C42×C73 | C8 | semidirect |
| 72. #64408 | C4⋊C8 | semidirect |
| 76. C4×C73 | C4×C8 | semidirect |
| 77. C4×C73 | C4⋊C8 | semidirect |
| 79. Dic73 | C4×C8 | semidirect |
| 80. Dic73 | C4⋊C8 | semidirect |
| 89. C73 | C4×C4⋊C8 | semidirect |
| 124. C42 | #10596842 | semidirect |
| 168. C4 | C4×#10596842 | semidirect |
| 169. C4 | C4⋊#10596842 | direct (N × H) |