Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
1640 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1640 conjugacy classes of subgroups — too many to draw. Only its 565 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D47 |
| commutator | C22×C47 | C25 |
| Frattini | C22 | C24×D47 |
| Fitting | C22×C4⋊C4×C47 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | C22×C4⋊C4 | D47 |
| hypocenter | C47 | C2×#537 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C22×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#10625350 | C2 | semidirect |
| 2. #15689704 | C2 | direct (N × H) |
| 3. C2×#13094004 | C2 | semidirect |
| 4. C2×#13093999 | C2 | semidirect |
| 5. C2×#13093998 | C2 | semidirect |
| 6. C22×C4⋊C4×C47 | C2 | semidirect |
| 8. C2×#10625350 | C22 | semidirect |
| 14. #13094004 | C22 | semidirect |
| 15. #13093999 | C22 | semidirect |
| 16. #13093998 | C22 | semidirect |
| 22. C2×C4⋊C4×C47 | C22 | semidirect |
| 26. C22×C4×C47 | D4 | semidirect |
| 58. C2×C4×C47 | C2×D4 | semidirect |
| 85. C2×C47 | #537 | semidirect |
| 95. C22×C4⋊C4 | D47 | semidirect |
| 96. C47 | C2×#537 | semidirect |
| 111. C2×C4⋊C4 | C2×D47 | semidirect |
| 128. C22×C4 | D188 | semidirect |
| 155. C2×C4 | C2×D188 | semidirect |
| 175. C2 | #15689704 | direct (N × H) |