Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
434 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 121 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 | #477×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | #477 | D73 |
| hypocenter | C73 | #3106 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #477 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17989138 | C2 | semidirect |
| 2. C4×#11924029 | C2 | semidirect |
| 3. #17988914 | C2 | semidirect |
| 4. #17988874 | C2 | semidirect |
| 5. #17988787 | C2 | semidirect |
| 6. #17988783 | C2 | semidirect |
| 7. #17988735 | C2 | semidirect |
| 8. #17988672 | C2 | semidirect |
| 9. #17988669 | C2 | semidirect |
| 10. #17988639 | C2 | semidirect |
| 11. #477×C73 | C2 | semidirect |
| 88. Q8×C73 | #41 | semidirect |
| 106. D292 | #41 | semidirect |
| 145. C73 | #3106 | semidirect |
| 149. #477 | D73 | semidirect |
| 233. Q8 | #11924029 | semidirect |