Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
704 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 233 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 | C22×C73 | C23×C4 |
| Fitting | #382×C73 | C2 |
| socle | C23×C73 | C24 |
| hypercenter | #382 | D73 |
| hypocenter | C73 | #2349 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #382 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #17988483 | C2 | semidirect |
| 4. #17988461 | C2 | semidirect |
| 5. #17988446 | C2 | semidirect |
| 6. C4×C4⋊Dic73 | C2 | semidirect |
| 7. #95×D73 | C2 | semidirect |
| 8. #382×C73 | C2 | semidirect |
| 12. C4×D292 | C4 | semidirect |
| 38. C2×C4×D73 | C2×C4 | semidirect |
| 40. C4⋊Dic73 | C2×C4 | semidirect |
| 43. #11924005 | C2×C4 | semidirect |
| 50. C42×C73 | C2×C4 | semidirect |
| 75. D292 | C4⋊C4 | semidirect |
| 102. C73 | #2349 | semidirect |
| 107. #382 | D73 | semidirect |
| 152. C42 | C4×D73 | semidirect |