Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
420 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 133 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 | #2644 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17988515 | C2 | semidirect |
| 2. #17988515 | C2 | semidirect |
| 3. #17988512 | C2 | semidirect |
| 4. #17988510 | C2 | semidirect |
| 7. #17988486 | C2 | semidirect |
| 8. #17988485 | C2 | semidirect |
| 9. #17988483 | C2 | semidirect |
| 10. #17988433 | C2 | semidirect |
| 136. C73 | #2644 | semidirect |