Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
336 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 98 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 | C22⋊C8×C73 | C4 |
| hypercenter | C22⋊C8 | #64408 |
| hypocenter | C73 | #1750 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C22⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#14556645 | C2 | semidirect |
| 4. C2×C8×#64408 | C2 | semidirect |
| 5. #17989452 | C2 | semidirect |
| 6. #17989452 | C2 | semidirect |
| 16. #14556648 | C4 | semidirect |
| 17. C22⋊#10596833 | C4 | semidirect |
| 23. C22⋊#10596831 | C4 | semidirect |
| 24. #14556503 | C4 | semidirect |
| 25. #14556503 | C4 | semidirect |
| 26. C22⋊C8×C73 | C4 | semidirect |
| 126. C73 | #1750 | semidirect |
| 150. C22⋊C8 | #64408 | semidirect |