Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
1224 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 237 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 | C24×C4×C47 | C2 |
| hypercenter | C24×C4 | D47 |
| hypocenter | C47 | #2847 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C24×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13093998 | C2 | semidirect |
| 2. C2×#13093993 | C2 | semidirect |
| 3. #15689002 | C2 | semidirect |
| 4. #15688983 | C2 | semidirect |
| 5. C24×C4×C47 | C2 | semidirect |
| 6. C22×D188 | C22 | semidirect |
| 10. C2×C4⋊Dic47 | C22 | semidirect |
| 12. C2×(C2×D47)⋊C4 | C22 | semidirect |
| 13. C47⋊#95 | C22 | semidirect |
| 20. C24×C47 | D4 | semidirect |
| 27. C22×C4×C47 | D4 | semidirect |
| 65. C22×C47 | #121 | semidirect |
| 73. C4×C47 | #120 | semidirect |
| 81. C24×C4 | D47 | semidirect |
| 86. C47 | #2847 | semidirect |
| 102. C24 | D188 | semidirect |
| 113. C22×C4 | C22⋊D47 | semidirect |
| 149. C22 | #13093998 | semidirect |
| 155. C4 | #13093993 | semidirect |