Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
612 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 157 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 | #384×C73 | C2 |
| hypercenter | #384 | D73 |
| hypocenter | C73 | #2620 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556579 | C2 | semidirect |
| 2. C2×#14556571 | C2 | semidirect |
| 4. C2×#14556548 | C2 | semidirect |
| 5. #17988509 | C2 | semidirect |
| 6. #17988504 | C2 | semidirect |
| 7. #17988492 | C2 | semidirect |
| 8. #17988488 | C2 | semidirect |
| 9. #384×C73 | C2 | semidirect |
| 62. C42×C73 | D4 | semidirect |
| 127. C73 | #2620 | semidirect |
| 136. #384 | D73 | semidirect |
| 189. C42 | D292 | semidirect |