Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
912 conjugacy classes of subgroups; only the 290 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 290 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#64408 |
| commutator | C2×C73 | C22×C42 |
| Fitting | C2×C22⋊C4×C73 | C4 |
| socle | C22×C73 | C23×C4 |
| hypercenter | C2×C22⋊C4 | #64408 |
| hypocenter | C73 | #2273 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22⋊C4×#64408 | C2 | semidirect |
| 3. C4×C22⋊#64408 | C2 | semidirect |
| 6. C2×C22⋊#64408 | C4 | semidirect |
| 9. C2×C4×#64408 | C22 | semidirect |
| 10. (C2×#64408)⋊C4 | C22 | semidirect |
| 13. C2×C22⋊Dic73 | C4 | semidirect |
| 14. C2×#11924005 | C4 | semidirect |
| 15. C22⋊C4×D73 | C4 | semidirect |
| 17. C2×C22⋊C4×C73 | C4 | semidirect |
| 19. C22×#64408 | C2×C4 | semidirect |
| 21. C22⋊#64408 | C2×C4 | semidirect |
| 22. C22⋊#64408 | C2×C4 | semidirect |
| 30. C22×Dic73 | C2×C4 | semidirect |
| 32. C2×C4×D73 | C2×C4 | semidirect |
| 34. C22⋊Dic73 | C2×C4 | semidirect |
| 35. #11924005 | C2×C4 | semidirect |
| 37. C22×C4×C73 | C2×C4 | semidirect |
| 38. C22⋊C4×C73 | C2×C4 | semidirect |
| 40. C23×C73 | C42 | semidirect |
| 48. C22×D73 | C42 | semidirect |
| 49. C22×D73 | C42 | semidirect |
| 93. C73 | #2273 | semidirect |
| 108. C2×C22⋊C4 | #64408 | semidirect |
| 125. C22×C4 | C2×#64408 | semidirect |
| 130. C22⋊C4 | C2×#64408 | semidirect |
| 146. C23 | C4×#64408 | semidirect |