Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
1348 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 1348 conjugacy classes of subgroups — too many to draw. Only its 213 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 | C23×D4×C47 | C2 |
| hypercenter | C23×D4 | D47 |
| hypocenter | C47 | #2433 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13094020 | C2 | semidirect |
| 2. C2×#13093998 | C2 | semidirect |
| 3. C2×#13093993 | C2 | semidirect |
| 4. #15689031 | C2 | semidirect |
| 5. #15689026 | C2 | semidirect |
| 6. C4×C22⋊Dic47 | C2 | semidirect |
| 7. C23×D4×C47 | C2 | semidirect |
| 8. C22×D188 | C22 | semidirect |
| 10. C22×C22⋊D47 | C22 | semidirect |
| 14. C2×C4⋊Dic47 | C22 | semidirect |
| 16. C2×C22⋊Dic47 | C22 | semidirect |
| 17. C2×(C2×D47)⋊C4 | C22 | semidirect |
| 18. C2×C4×Dic47 | C22 | semidirect |
| 19. C47⋊#95 | C22 | semidirect |
| 38. C2×D4×C47 | D4 | semidirect |
| 40. C22×C4×C47 | D4 | semidirect |
| 53. C22⋊Dic47 | D4 | semidirect |
| 88. C2×Dic47 | C2×D4 | semidirect |
| 99. C22×C47 | #127 | semidirect |
| 109. C4×C47 | #120 | semidirect |
| 120. C23×D4 | D47 | semidirect |
| 127. C47 | #2433 | semidirect |
| 165. C2×D4 | C22⋊D47 | semidirect |
| 169. C22×C4 | C22⋊D47 | semidirect |
| 223. C22 | #13094020 | semidirect |
| 231. C4 | #13093993 | semidirect |