Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
516 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 229 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 | C22×C47 | C23×C4 |
| Fitting | C2×#126×C47 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | C2×#126 | D47 |
| hypocenter | C47 | C4×#126 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C2×#126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #15689009 | C2 | semidirect |
| 3. #15688991 | C2 | semidirect |
| 4. C4⋊C4×Dic47 | C2 | semidirect |
| 6. C42×Dic47 | C2 | semidirect |
| 18. #126×C47 | C4 | semidirect |
| 30. C4⋊C4×C47 | C2×C4 | semidirect |
| 32. C42×C47 | C2×C4 | semidirect |
| 68. Dic47 | #126 | direct (N × H) |
| 81. C47 | C4×#126 | semidirect |
| 83. #126 | Dic47 | direct (N × H) |
| 105. C4⋊C4 | C2×Dic47 | semidirect |
| 111. C42 | C2×Dic47 | semidirect |