Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
276 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 85 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×Q8⋊C8 | C2 |
| socle | C22×C47 | C2×C22⋊C4 |
| hypercenter | Q8⋊C8 | D47 |
| hypocenter | C47 | #1476 |
| LCS | G ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #15689175 | C2 | semidirect |
| 3. C4×C8×D47 | C2 | semidirect |
| 4. Q8⋊(C47⋊C8) | C2 | semidirect |
| 5. #15688852 | C2 | semidirect |
| 6. #15688850 | C2 | semidirect |
| 7. C47×Q8⋊C8 | C2 | semidirect |
| 29. #10625354 | C8 | semidirect |
| 60. Q8×C47 | C2×C8 | semidirect |
| 72. D188 | C2×C8 | semidirect |
| 114. Q8⋊C8 | D47 | semidirect |
| 117. C47 | #1476 | semidirect |
| 170. Q8 | C8×D47 | semidirect |