Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
4632 conjugacy classes of subgroups; only the 1106 normal subgroups are shown.
This group has 4632 conjugacy classes of subgroups — too many to draw. Only its 1106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×#64408 |
| commutator | C2×C73 | C24×C4 |
| Frattini | C2 | C24×#64408 |
| Fitting | C25×C73 | C4 |
| socle | C24×C73 | C2×C4 |
| hypercenter | C25 | #64408 |
| hypocenter | C73 | C23×C22⋊C4 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C24 ◁ C25 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×#64408 | C2 | semidirect |
| 2. C22×C22⋊#64408 | C2 | direct (N × H) |
| 5. C23×#64408 | C22 | semidirect |
| 6. C2×C22⋊#64408 | C22 | direct (N × H) |
| 8. C24×D73 | C4 | semidirect |
| 9. C24×D73 | C4 | semidirect |
| 12. C25×C73 | C4 | semidirect |
| 14. C22×#64408 | C23 | semidirect |
| 15. C22⋊#64408 | C23 | direct (N × H) |
| 20. C23×D73 | C2×C4 | semidirect |
| 21. C23×D73 | C2×C4 | semidirect |
| 27. C24×C73 | C2×C4 | semidirect |
| 29. C23×C73 | C22⋊C4 | semidirect |
| 31. C23×C73 | C22×C4 | semidirect |
| 35. C22×D73 | C22⋊C4 | semidirect |
| 37. C22×D73 | C22×C4 | semidirect |
| 38. C22×D73 | C22×C4 | semidirect |
| 43. C2×#64408 | C24 | semidirect |
| 45. C22×C73 | C2×C22⋊C4 | semidirect |
| 47. C22×C73 | C23×C4 | semidirect |
| 51. C2×D73 | C2×C22⋊C4 | semidirect |
| 53. C2×D73 | C23×C4 | semidirect |
| 58. C2×C73 | C22×C22⋊C4 | semidirect |
| 61. D73 | C22×C22⋊C4 | semidirect |
| 64. C73 | C23×C22⋊C4 | semidirect |
| 73. C25 | #64408 | semidirect |
| 88. C24 | C2×#64408 | semidirect |
| 103. C23 | C22⋊#64408 | direct (N × H) |
| 105. C23 | C22×#64408 | semidirect |
| 117. C22 | C2×C22⋊#64408 | direct (N × H) |
| 119. C22 | C23×#64408 | semidirect |
| 125. C2 | C22×C22⋊#64408 | direct (N × H) |