Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
484 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D292 |
| commutator | C4×C73 | C23×C4 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | #405×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | #405 | D73 |
| hypocenter | C73 | #2951 |
| LCS | G ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #405 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17989067 | C2 | semidirect |
| 3. #17988689 | C2 | semidirect |
| 4. C4×Dic292 | C2 | semidirect |
| 5. C4×D584 | C2 | semidirect |
| 6. C2×#14556525 | C2 | semidirect |
| 7. #17988589 | C2 | semidirect |
| 8. #405×C73 | C2 | semidirect |
| 10. #14556613 | C4 | semidirect |
| 30. #11924028 | C2×C4 | semidirect |
| 37. Dic292 | C2×C4 | semidirect |
| 38. #11924017 | C2×C4 | semidirect |
| 39. D584 | C2×C4 | semidirect |
| 47. C2×C8×C73 | C2×C4 | semidirect |
| 96. C73 | #2951 | semidirect |
| 104. #405 | D73 | semidirect |
| 138. C2×C8 | C4×D73 | semidirect |