Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
456 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D73 |
| commutator | C4×C73 | C23×C4 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | #441×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | #441 | D73 |
| hypocenter | C73 | #2950 |
| LCS | G ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #441 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #17988695 | C2 | semidirect |
| 4. #17988694 | C2 | semidirect |
| 5. #17988693 | C2 | semidirect |
| 6. C4×#11924018 | C2 | semidirect |
| 7. #17988679 | C2 | semidirect |
| 11. #441×C73 | C2 | semidirect |
| 15. Q16×D73 | C4 | semidirect |
| 109. C73 | #2950 | semidirect |
| 115. #441 | D73 | semidirect |