Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
928 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 233 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 | C22×C73 | C23×C4 |
| Fitting | #380×C73 | C2 |
| socle | C23×C73 | C24 |
| hypercenter | #380 | D73 |
| hypocenter | C73 | #2339 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14556553 | C2 | semidirect |
| 3. #17988492 | C2 | semidirect |
| 4. #17988463 | C2 | semidirect |
| 5. #17988449 | C2 | semidirect |
| 6. C4×C22⋊Dic73 | C2 | semidirect |
| 7. #95×D73 | C2 | semidirect |
| 8. #380×C73 | C2 | semidirect |
| 10. C2×#11924028 | C4 | semidirect |
| 31. C2×Dic146 | C2×C4 | semidirect |
| 35. C2×C22⋊D73 | C2×C4 | semidirect |
| 43. C2×C4×D73 | C2×C4 | semidirect |
| 49. C22×C4×C73 | C2×C4 | semidirect |
| 82. C2×Dic73 | #41 | semidirect |
| 83. D292 | C22⋊C4 | semidirect |
| 116. C73 | #2339 | semidirect |
| 122. #380 | D73 | semidirect |
| 162. C22×C4 | C4×D73 | semidirect |