Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
780 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 325 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 | C2×C73 | C22×C42 |
| Fitting | C4×C4⋊C4×C73 | C2 |
| socle | C23×C73 | C24 |
| hypercenter | C4×C4⋊C4 | D73 |
| hypocenter | C73 | #2275 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C4×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C4⋊C4×Dic73 | C2 | semidirect |
| 4. C4×#11924005 | C2 | semidirect |
| 5. #17988434 | C2 | semidirect |
| 6. #17988433 | C2 | semidirect |
| 7. #95×D73 | C2 | semidirect |
| 8. C4×C4⋊C4×C73 | C2 | semidirect |
| 12. C4×D292 | C4 | semidirect |
| 13. #14556553 | C4 | semidirect |
| 36. C2×C4×D73 | C2×C4 | semidirect |
| 37. C2×C4×D73 | C2×C4 | semidirect |
| 38. C4⋊Dic73 | C2×C4 | semidirect |
| 39. #11924005 | C2×C4 | semidirect |
| 40. #11924005 | C2×C4 | semidirect |
| 42. C4×Dic73 | C2×C4 | semidirect |
| 47. C4⋊C4×C73 | C2×C4 | semidirect |
| 49. C42×C73 | C2×C4 | semidirect |
| 74. D292 | C42 | semidirect |
| 101. C73 | #2275 | semidirect |
| 105. C4×C4⋊C4 | D73 | semidirect |
| 144. C4⋊C4 | C4×D73 | semidirect |
| 150. C42 | C4×D73 | semidirect |