Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
754 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 754 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 | C22 | C22×D292 |
| commutator | C2×C4×C73 | C24 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | #407×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | #407 | D73 |
| hypocenter | C73 | #3007 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ #407 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14556624 | C2 | semidirect |
| 3. C2×#14556570 | C2 | semidirect |
| 4. #17988751 | C2 | semidirect |
| 5. #17988745 | C2 | semidirect |
| 6. #17988740 | C2 | semidirect |
| 7. #17988589 | C2 | semidirect |
| 8. #407×C73 | C2 | semidirect |
| 15. C22×Dic146 | C22 | semidirect |
| 20. C2×Dic292 | C22 | semidirect |
| 21. C2×#11924017 | C22 | semidirect |
| 25. #14556570 | C22 | semidirect |
| 26. C2×C4⋊Dic73 | C22 | semidirect |
| 29. #14556516 | C22 | semidirect |
| 30. #14556513 | C22 | semidirect |
| 32. C2×M16×C73 | C22 | semidirect |
| 34. C22⋊C8×C73 | C22 | semidirect |
| 126. C22×C73 | #137 | semidirect |
| 147. C73 | #3007 | semidirect |
| 155. #407 | D73 | semidirect |
| 170. C2×M16 | C2×D73 | semidirect |
| 181. C22⋊C8 | C2×D73 | semidirect |
| 277. C22 | #14556624 | semidirect |