Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D73 |
| commutator | C2×C4×C73 | C24 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | #496×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | #496 | D73 |
| hypocenter | C73 | #3153 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #496 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556620 | C2 | semidirect |
| 2. C2×#14556615 | C2 | semidirect |
| 3. #17989135 | C2 | semidirect |
| 4. #124×D73 | C2 | semidirect |
| 5. #17988982 | C2 | semidirect |
| 6. #17988981 | C2 | semidirect |
| 7. #17988974 | C2 | semidirect |
| 8. #17988970 | C2 | semidirect |
| 9. #17988968 | C2 | semidirect |
| 10. #17988539 | C2 | semidirect |
| 11. #496×C73 | C2 | semidirect |
| 17. C2×Dic292 | C22 | semidirect |
| 18. C2×#11924018 | C22 | semidirect |
| 21. C2×#11924016 | C22 | semidirect |
| 24. #14556591 | C22 | semidirect |
| 28. #14556578 | C22 | semidirect |
| 34. #14556502 | C22 | semidirect |
| 35. C8×Dic73 | C22 | semidirect |
| 36. C2×SD16×C73 | C22 | semidirect |
| 38. #127×C73 | C22 | semidirect |
| 40. #97×C73 | C22 | semidirect |
| 62. #11924011 | D4 | semidirect |
| 135. C73 | #3153 | semidirect |
| 143. #496 | D73 | semidirect |
| 157. C2×SD16 | C2×D73 | semidirect |
| 162. #127 | C2×D73 | semidirect |
| 174. #97 | C2×D73 | semidirect |