Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
1056 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 185 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×D47 |
| commutator, socle | C23×C47 | C24 |
| Fitting | C22×#41×C47 | C2 |
| hypercenter | C22×#41 | D47 |
| hypocenter | C47 | #2404 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13093992 | C2 | semidirect |
| 2. C22×(C2×D47)⋊C4 | C2 | semidirect |
| 3. #15689034 | C2 | semidirect |
| 4. #15689031 | C2 | semidirect |
| 5. #15689003 | C2 | semidirect |
| 6. #15689002 | C2 | semidirect |
| 7. #15688986 | C2 | semidirect |
| 8. C22×#41×C47 | C2 | semidirect |
| 14. C2×C22⋊Dic47 | C22 | semidirect |
| 19. C47⋊#95 | C22 | semidirect |
| 20. C47⋊#95 | C22 | semidirect |
| 21. C47⋊#95 | C22 | semidirect |
| 24. C22×Q8×C47 | C22 | semidirect |
| 26. C22×D4×C47 | C22 | semidirect |
| 28. C23×C4×C47 | C22 | semidirect |
| 43. C2×D4×C47 | D4 | semidirect |
| 48. C22×C4×C47 | D4 | semidirect |
| 82. C22×D47 | #41 | semidirect |
| 134. C22×#41 | D47 | semidirect |
| 142. C47 | #2404 | semidirect |
| 146. C22×Q8 | C2×D47 | semidirect |
| 149. C22×D4 | C2×D47 | semidirect |
| 152. C23×C4 | C2×D47 | semidirect |
| 180. C2×D4 | C22⋊D47 | semidirect |
| 189. C22×C4 | C22⋊D47 | semidirect |