Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
192 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×D47 |
| commutator | C4×C47 | C22×C8 |
| Frattini | C42 | C22×D47 |
| Fitting | C47×D4⋊C8 | C2 |
| socle | C22×C47 | C4×D4 |
| hypercenter | D4⋊C8 | D47 |
| hypocenter | C47 | #1580 |
| LCS | G ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. D4×C47⋊C8 | C2 | semidirect |
| 3. #15689188 | C2 | semidirect |
| 4. #15688873 | C2 | semidirect |
| 5. #15688852 | C2 | semidirect |
| 6. #15688845 | C2 | semidirect |
| 7. C47×D4⋊C8 | C2 | semidirect |
| 32. #10625334 | C8 | semidirect |
| 45. D4×C47 | C2×C8 | semidirect |
| 54. D188 | C2×C8 | semidirect |
| 63. C47⋊C8 | C2×C8 | semidirect |
| 89. D4⋊C8 | D47 | semidirect |
| 91. C47 | #1580 | semidirect |
| 131. D4 | C8×D47 | semidirect |