Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
680 conjugacy classes of subgroups; only the 338 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 338 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×#64408 |
| commutator | C2×C73 | C22×C42 |
| Frattini | C4 | C23×#64408 |
| Fitting | C22×C8×C73 | C4 |
| socle | C23×C73 | C42 |
| hypercenter | C22×C8 | #64408 |
| hypocenter | C73 | C22×#97 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#14556645 | C2 | direct (N × H) |
| 6. C2×#11924036 | C4 | semidirect |
| 8. C22×#10596833 | C4 | semidirect |
| 11. #14556645 | C22 | direct (N × H) |
| 13. C22×#10596831 | C4 | semidirect |
| 14. C2×C8×D73 | C4 | semidirect |
| 16. C22×C8×C73 | C4 | semidirect |
| 19. #11924036 | C2×C4 | semidirect |
| 21. C2×#10596833 | C2×C4 | semidirect |
| 30. C2×#10596831 | C2×C4 | semidirect |
| 31. C8×D73 | C2×C4 | semidirect |
| 34. C2×C8×C73 | C2×C4 | semidirect |
| 50. #10596833 | C22×C4 | semidirect |
| 51. C8×C73 | C22×C4 | semidirect |
| 52. #10596831 | C22×C4 | semidirect |
| 53. C22×C73 | #97 | semidirect |
| 55. C2×D73 | #97 | semidirect |
| 64. C2×C73 | C2×#97 | semidirect |
| 66. D73 | C2×#97 | semidirect |
| 69. C73 | C22×#97 | semidirect |
| 82. C22×C8 | #64408 | semidirect |
| 101. C2×C8 | C2×#64408 | semidirect |
| 121. C8 | C22×#64408 | semidirect |
| 126. C22 | #14556645 | direct (N × H) |
| 135. C2 | C2×#14556645 | direct (N × H) |