Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D47 |
| commutator | C22×C47 | C25 |
| Frattini | C22 | C24×D47 |
| Fitting | C2×C4⋊Q8×C47 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | C2×C4⋊Q8 | D47 |
| hypocenter | C47 | C2×#541 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15689734 | C2 | direct (N × H) |
| 3. C2×#13094016 | C2 | semidirect |
| 4. C2×#13094014 | C2 | semidirect |
| 6. C2×Q8×Dic47 | C2 | semidirect |
| 8. C2×C4⋊Q8×C47 | C2 | semidirect |
| 11. #13094016 | C22 | semidirect |
| 12. #13094014 | C22 | semidirect |
| 14. Q8×Dic47 | C22 | semidirect |
| 26. C4⋊Q8×C47 | C22 | semidirect |
| 82. C2×C47 | #541 | semidirect |
| 87. C2×C4⋊Q8 | D47 | semidirect |
| 94. C47 | C2×#541 | semidirect |
| 97. C4⋊Q8 | C2×D47 | semidirect |
| 168. C2 | #15689734 | direct (N × H) |