Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
836 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 173 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 | #390×C73 | C2 |
| hypercenter | #390 | D73 |
| hypocenter | C73 | #2432 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14556591 | C2 | semidirect |
| 3. C2×#14556578 | C2 | semidirect |
| 4. C2×#14556571 | C2 | semidirect |
| 5. #17988503 | C2 | semidirect |
| 6. #17988492 | C2 | semidirect |
| 7. #17988462 | C2 | semidirect |
| 8. C4×#11924005 | C2 | semidirect |
| 9. #390×C73 | C2 | semidirect |
| 89. C2×C4×C73 | #41 | semidirect |
| 137. C73 | #2432 | semidirect |
| 144. #390 | D73 | semidirect |
| 243. C2×C4 | #11924027 | semidirect |