Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
1320 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1320 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 | C24 | C22×D47 |
| commutator | C22×C47 | C25 |
| Frattini | C22 | C24×D47 |
| Fitting | C22×C22⋊C4×C47 | C2 |
| socle | C24×C47 | C23 |
| hypercenter | C22×C22⋊C4 | D47 |
| hypocenter | C47 | C22×#126 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C24 ◁ C22×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13094017 | C2 | direct (N × H) |
| 2. C22×C4⋊Dic47 | C2 | semidirect |
| 3. C22×Dic47⋊C4 | C2 | semidirect |
| 4. C22×Dic47⋊C4 | C2 | semidirect |
| 7. C22×C4×Dic47 | C2 | semidirect |
| 13. #13094017 | C22 | direct (N × H) |
| 14. C2×C4⋊Dic47 | C22 | semidirect |
| 15. C2×Dic47⋊C4 | C22 | semidirect |
| 16. C2×Dic47⋊C4 | C22 | semidirect |
| 19. C2×C4×Dic47 | C22 | semidirect |
| 44. C4⋊Dic47 | C23 | semidirect |
| 45. Dic47⋊C4 | C23 | semidirect |
| 46. Dic47⋊C4 | C23 | semidirect |
| 47. C4×Dic47 | C23 | semidirect |
| 73. C22×C47 | #126 | semidirect |
| 86. C2×C47 | C2×#126 | semidirect |
| 98. C47 | C22×#126 | semidirect |
| 163. C22 | #13094017 | direct (N × H) |
| 175. C2 | C2×#13094017 | direct (N × H) |