Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
516 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D73 |
| commutator | C22×C73 | C23×C4 |
| Frattini | C23 | C23×D73 |
| Fitting | C43×C73 | C2 |
| socle | C23×C73 | C24 |
| hypercenter | C43 | D73 |
| hypocenter | C73 | C4×#126 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22×C4 ◁ C43 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #17988471 | C2 | semidirect |
| 4. #17988455 | C2 | semidirect |
| 5. C4×#11924007 | C2 | semidirect |
| 7. C43×C73 | C2 | semidirect |
| 9. #14556585 | C4 | direct (N × H) |
| 28. #11924007 | C2×C4 | semidirect |
| 37. C42×C73 | C2×C4 | semidirect |
| 65. C4×C73 | #126 | semidirect |
| 74. C73 | C4×#126 | semidirect |
| 81. C43 | D73 | semidirect |
| 111. C42 | C4×D73 | semidirect |
| 142. C4 | #14556585 | direct (N × H) |