Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
196 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 101 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×M32 |
| 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 |
|---|---|---|
| 2. #17989681 | C2 | semidirect |
| 3. C4×#11924040 | C2 | semidirect |
| 5. #14556688 | C4 | direct (N × H) |
| 14. #11924040 | C2×C4 | semidirect |
| 49. C4×C73 | M32 | semidirect |
| 51. Dic73 | M32 | semidirect |
| 59. C73 | C4×M32 | semidirect |
| 112. C4 | #14556688 | direct (N × H) |