Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
480 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#64408 |
| commutator, socle | C22×C73 | C2×C42 |
| Fitting | C2×M16×C73 | C4 |
| hypercenter | C2×M16 | #64408 |
| hypocenter | C73 | #1728 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C2×M16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #17989452 | C2 | semidirect |
| 6. C2×#11924038 | C4 | semidirect |
| 9. C2×#11924037 | C4 | semidirect |
| 16. C2×#11924012 | C4 | semidirect |
| 17. C2×#11924011 | C4 | semidirect |
| 21. C2×M16×C73 | C4 | semidirect |
| 29. C2×#10596833 | C2×C4 | semidirect |
| 45. C2×#10596831 | C2×C4 | semidirect |
| 50. C2×C8×C73 | C2×C4 | semidirect |
| 60. C2×#64408 | M16 | semidirect |
| 106. C73 | #1728 | semidirect |
| 121. C2×M16 | #64408 | semidirect |
| 153. C2×C8 | C2×#64408 | semidirect |