Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
900 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 900 conjugacy classes of subgroups — too many to draw. Only its 173 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 | #2539 |
| 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 |
|---|---|---|
| 1. C2×#14556574 | C2 | semidirect |
| 2. C2×#14556565 | C2 | semidirect |
| 3. C2×#14556560 | C2 | semidirect |
| 4. #17988523 | C2 | semidirect |
| 5. #17988496 | C2 | semidirect |
| 6. #17988487 | C2 | semidirect |
| 7. C4×C22⋊Dic73 | C2 | semidirect |
| 8. C22×C22⋊C4×C73 | C2 | semidirect |
| 9. C22×D292 | C22 | semidirect |
| 15. C2×C4⋊Dic73 | C22 | semidirect |
| 16. C2×#11924007 | C22 | semidirect |
| 19. C2×#11924005 | C22 | semidirect |
| 20. C2×#11924005 | C22 | semidirect |
| 21. C2×C4×Dic73 | C22 | semidirect |
| 22. #14556498 | C22 | semidirect |
| 43. C22⋊Dic73 | D4 | semidirect |
| 56. C22×C4×C73 | D4 | semidirect |
| 130. C73 | #2539 | semidirect |
| 134. C22×C22⋊C4 | D73 | semidirect |
| 179. C22×C4 | C22⋊D73 | semidirect |