Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
672 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 153 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, socle | C23×C73 | C24 |
| Fitting | C4×C22⋊C4×C73 | C2 |
| hypercenter | C4×C22⋊C4 | D73 |
| hypocenter | C73 | #2561 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556570 | C2 | semidirect |
| 3. #17988514 | C2 | semidirect |
| 4. #17988500 | C2 | semidirect |
| 5. #17988478 | C2 | semidirect |
| 6. #17988448 | C2 | semidirect |
| 8. C4×C22⋊C4×C73 | C2 | semidirect |
| 10. C22×Dic146 | C22 | semidirect |
| 13. C2×C4⋊Dic73 | C22 | semidirect |
| 14. C2×#11924007 | C22 | semidirect |
| 21. #14556498 | C22 | semidirect |
| 22. #14556498 | C22 | semidirect |
| 25. C2×C42×C73 | C22 | semidirect |
| 26. #95×C73 | C22 | semidirect |
| 111. C73 | #2561 | semidirect |
| 119. C4×C22⋊C4 | D73 | semidirect |
| 134. C2×C42 | C2×D73 | semidirect |
| 137. #95 | C2×D73 | semidirect |