Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
582 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D73 |
| commutator, socle | C23×C73 | C24 |
| Fitting | C2×C4×D4×C73 | C2 |
| hypercenter | C2×C4×D4 | D73 |
| hypocenter | C73 | #2603 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C2×C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556585 | C2 | semidirect |
| 2. #17988518 | C2 | semidirect |
| 3. #17988513 | C2 | semidirect |
| 4. #17988501 | C2 | semidirect |
| 6. #17988487 | C2 | semidirect |
| 7. #17988481 | C2 | semidirect |
| 8. #17988466 | C2 | semidirect |
| 9. #17988460 | C2 | semidirect |
| 10. #17988433 | C2 | semidirect |
| 11. C2×C4×D4×C73 | C2 | semidirect |
| 70. C42×C73 | D4 | semidirect |
| 144. C73 | #2603 | semidirect |
| 146. C2×C4×D4 | D73 | semidirect |
| 214. C42 | C22⋊D73 | semidirect |