Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
368 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 191 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×#10596842 |
| commutator | C2×C73 | C23×C8 |
| Frattini | C2 | C23×#10596842 |
| Fitting | C2×D4×C73 | C8 |
| socle | C22×C73 | C22×C8 |
| hypercenter | C2×D4 | #10596842 |
| hypocenter | C73 | C2×#504 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17989708 | C2 | direct (N × H) |
| 2. C2×#14556688 | C2 | semidirect |
| 3. C2×#14556687 | C2 | semidirect |
| 4. C2×#14556686 | C2 | semidirect |
| 5. C22×#11924040 | C2 | semidirect |
| 7. #14556688 | C22 | semidirect |
| 8. #14556687 | C22 | semidirect |
| 9. #14556686 | C22 | semidirect |
| 13. C2×#11924040 | C22 | semidirect |
| 66. C2×C73 | #504 | semidirect |
| 70. C73 | C2×#504 | semidirect |
| 137. C2 | #17989708 | direct (N × H) |