Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
1224 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 209 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 | C2×#120×C47 | C2 |
| hypercenter | C2×#120 | D47 |
| hypocenter | C47 | #2847 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×Dic47 | C2 | semidirect |
| 2. C2×#13093996 | C2 | semidirect |
| 3. C2×#13093993 | C2 | semidirect |
| 4. #15689003 | C2 | semidirect |
| 5. #15689000 | C2 | semidirect |
| 6. #15688981 | C2 | semidirect |
| 7. C2×#120×C47 | C2 | semidirect |
| 9. C22×C22⋊D47 | C22 | semidirect |
| 15. C2×Dic47⋊C4 | C22 | semidirect |
| 17. C2×C22⋊Dic47 | C22 | semidirect |
| 18. C2×(C2×D47)⋊C4 | C22 | semidirect |
| 19. C47⋊#95 | C22 | semidirect |
| 26. C24×C47 | D4 | semidirect |
| 42. C22×Dic47 | D4 | semidirect |
| 88. C22×C47 | #121 | semidirect |
| 98. Dic47 | #120 | semidirect |
| 109. C2×#120 | D47 | semidirect |
| 113. C47 | #2847 | semidirect |
| 133. C24 | C22⋊D47 | semidirect |
| 197. C22 | #13093996 | semidirect |