Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
1160 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 210 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, socle | C22×C73 | C23×C4 |
| Fitting | C22×D4×C73 | C4 |
| hypercenter | C22×D4 | #64408 |
| hypocenter | C73 | #2308 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C22⋊#64408 | C2 | semidirect |
| 2. #17989535 | C2 | semidirect |
| 3. #17989530 | C2 | semidirect |
| 4. #17989528 | C2 | semidirect |
| 6. C23×#64408 | C22 | semidirect |
| 9. C2×C22⋊#64408 | C22 | semidirect |
| 10. C2×C22⋊#64408 | C22 | semidirect |
| 11. (C2×#64408)⋊C4 | C22 | semidirect |
| 14. C22×D292 | C4 | semidirect |
| 15. C22×C22⋊D73 | C4 | semidirect |
| 16. C22×C22⋊D73 | C4 | semidirect |
| 18. C2×D4×D73 | C4 | semidirect |
| 21. C22×D4×C73 | C4 | semidirect |
| 33. C23×D73 | C2×C4 | semidirect |
| 34. C23×D73 | C2×C4 | semidirect |
| 40. C2×D292 | C2×C4 | semidirect |
| 43. C2×C22⋊D73 | C2×C4 | semidirect |
| 44. C2×C22⋊D73 | C2×C4 | semidirect |
| 48. C22×Dic73 | C2×C4 | semidirect |
| 50. C2×C4×D73 | C2×C4 | semidirect |
| 53. C24×C73 | C2×C4 | semidirect |
| 55. C2×D4×C73 | C2×C4 | semidirect |
| 56. C22×C4×C73 | C2×C4 | semidirect |
| 60. C23×C73 | C22⋊C4 | semidirect |
| 76. C22×D73 | C22⋊C4 | semidirect |
| 77. C22×D73 | C22⋊C4 | semidirect |
| 136. C73 | #2308 | semidirect |
| 150. C22×D4 | #64408 | semidirect |
| 170. C24 | C2×#64408 | semidirect |
| 181. C2×D4 | C2×#64408 | semidirect |
| 189. C22×C4 | C2×#64408 | semidirect |
| 217. C23 | C22⋊#64408 | semidirect |