Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
816 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 816 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 | C2×C22⋊C4×C73 | C4 |
| hypercenter | C2×C22⋊C4 | #64408 |
| hypocenter | C73 | #2315 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17989534 | C2 | semidirect |
| 3. #17989529 | C2 | semidirect |
| 6. 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 |
| 31. C22×Dic73 | C2×C4 | semidirect |
| 33. C2×C4×D73 | C2×C4 | semidirect |
| 35. C22⋊Dic73 | C2×C4 | semidirect |
| 36. #11924005 | C2×C4 | semidirect |
| 38. C22×C4×C73 | C2×C4 | semidirect |
| 39. C22⋊C4×C73 | C2×C4 | semidirect |
| 41. C23×C73 | C4⋊C4 | semidirect |
| 50. C22×D73 | C4⋊C4 | semidirect |
| 51. C22×D73 | C4⋊C4 | semidirect |
| 99. C73 | #2315 | semidirect |
| 115. C2×C22⋊C4 | #64408 | semidirect |
| 132. C22×C4 | C2×#64408 | semidirect |
| 138. C22⋊C4 | C2×#64408 | semidirect |
| 155. C23 | C4⋊#64408 | semidirect |