Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
702 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 149 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 | C22×C22⋊C4×C73 | C2 |
| hypercenter | C22×C22⋊C4 | D73 |
| hypocenter | C73 | #2622 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C22×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17988515 | C2 | semidirect |
| 3. #17988502 | C2 | semidirect |
| 4. #17988466 | C2 | semidirect |
| 5. #17988460 | C2 | semidirect |
| 6. #17988443 | C2 | semidirect |
| 7. C22×C22⋊C4×C73 | C2 | semidirect |
| 11. C2×#11924007 | C22 | semidirect |
| 16. C2×#11924005 | C22 | semidirect |
| 17. #14556498 | C22 | semidirect |
| 18. #14556498 | C22 | semidirect |
| 98. C73 | #2622 | semidirect |
| 100. C22×C22⋊C4 | D73 | semidirect |