Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
760 conjugacy classes of subgroups; only the 434 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 434 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×C42 | #64408 |
| commutator, hypocenter | C73 | C22×C4×C8 |
| Frattini | C22 | C23×#64408 |
| Fitting | C2×C42×C73 | C4 |
| socle | C23×C73 | C22×C4 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#11924036 | C2 | direct (N × H) |
| 3. C2×C4×#10596833 | C2 | semidirect |
| 5. C2×#11924036 | C4 | direct (N × H) |
| 8. C4×#10596833 | C22 | semidirect |
| 16. #11924036 | C2×C4 | direct (N × H) |
| 17. C2×#10596833 | C2×C4 | semidirect |
| 22. C2×C4×D73 | C8 | semidirect |
| 38. C2×C4×C73 | C2×C8 | semidirect |
| 41. C2×Dic73 | C2×C8 | semidirect |
| 47. C4×D73 | C2×C8 | semidirect |
| 49. #10596833 | C22×C4 | semidirect |
| 53. C2×D73 | C4×C8 | semidirect |
| 57. C4×C73 | C22×C8 | semidirect |
| 59. Dic73 | C22×C8 | semidirect |
| 61. C2×C73 | C2×C4×C8 | semidirect |
| 64. D73 | C2×C4×C8 | semidirect |
| 66. C73 | C22×C4×C8 | semidirect |
| 112. C2×C4 | #11924036 | direct (N × H) |
| 126. C4 | C2×#11924036 | direct (N × H) |
| 128. C2 | C4×#11924036 | direct (N × H) |