Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
688 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 688 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, Frattini | C23 | C23×D73 |
| commutator, socle | C23×C73 | C24 |
| Fitting | C22×C42×C73 | C2 |
| hypercenter | C22×C42 | D73 |
| hypocenter | C73 | #2854 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556574 | C2 | semidirect |
| 3. #17988489 | C2 | semidirect |
| 4. #17988485 | C2 | semidirect |
| 5. #17988478 | C2 | semidirect |
| 6. #17988466 | C2 | semidirect |
| 7. #17988447 | C2 | semidirect |
| 8. C22×C42×C73 | C2 | semidirect |
| 50. C22×C4×C73 | D4 | semidirect |
| 107. C4×C73 | #123 | semidirect |
| 118. C73 | #2854 | semidirect |
| 121. C22×C42 | D73 | semidirect |
| 160. C22×C4 | D292 | semidirect |
| 227. C4 | #14556574 | semidirect |