Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
1476 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1476 conjugacy classes of subgroups — too many to draw. Only its 557 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D47 |
| commutator, socle | C22×C47 | C25 |
| Fitting | C4×#41×C47 | C2 |
| hypercenter | C4×#41 | D47 |
| hypocenter | C47 | #3499 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C4×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13094071 | C2 | semidirect |
| 2. Q8×D188 | C2 | semidirect |
| 3. #15689777 | C2 | semidirect |
| 4. #15689699 | C2 | semidirect |
| 5. #15689673 | C2 | semidirect |
| 6. C2×#13094024 | C2 | semidirect |
| 7. C4×#41×C47 | C2 | semidirect |
| 28. #41×C47 | D4 | semidirect |
| 78. C4×C47 | 2−1+4 | semidirect |
| 91. C4×#41 | D47 | semidirect |
| 92. C47 | #3499 | semidirect |
| 115. #41 | D188 | semidirect |
| 164. C4 | #13094071 | semidirect |