Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
372 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 130 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 | C4×#64408 |
| commutator | C4×C73 | C2×C42 |
| Frattini | C2×C4 | C22×#64408 |
| Fitting | C22×C8×C73 | C4 |
| socle | C22×C73 | #95 |
| hypercenter | C22×C8 | #64408 |
| hypocenter | C73 | C2×#338 |
| LCS | G ▷ C4×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17989456 | C2 | direct (N × H) |
| 89. C2×C73 | #338 | semidirect |
| 94. C73 | C2×#338 | semidirect |
| 185. C2 | #17989456 | direct (N × H) |