Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
280 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #10596842 |
| commutator, hypocenter | C73 | C2×C82 |
| Frattini | C4 | C22×#10596842 |
| Fitting | C2×C8×C73 | C8 |
| socle | C22×C73 | C4×C8 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C8×#10596842 | C2 | direct (N × H) |
| 12. C2×#10596842 | C8 | direct (N × H) |
| 15. #11924036 | C8 | semidirect |
| 17. C2×#10596833 | C8 | semidirect |
| 22. C2×#10596831 | C8 | semidirect |
| 23. C8×D73 | C8 | semidirect |
| 25. C2×C8×C73 | C8 | semidirect |
| 30. #10596842 | C2×C8 | direct (N × H) |
| 37. #10596833 | C2×C8 | semidirect |
| 38. C8×C73 | C2×C8 | semidirect |
| 39. #10596831 | C2×C8 | semidirect |
| 50. C2×C73 | C82 | semidirect |
| 52. D73 | C82 | semidirect |
| 55. C73 | C2×C82 | semidirect |
| 77. C2×C8 | #10596842 | direct (N × H) |
| 94. C8 | C2×#10596842 | direct (N × H) |
| 107. C2 | C8×#10596842 | direct (N × H) |