Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
702 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 149 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, socle | C23×C47 | C24 |
| Fitting | C22×C22⋊C4×C47 | C2 |
| hypercenter | C22×C22⋊C4 | D47 |
| hypocenter | C47 | #2622 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C22×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #15689051 | C2 | semidirect |
| 3. #15689038 | C2 | semidirect |
| 4. #15689002 | C2 | semidirect |
| 5. #15688996 | C2 | semidirect |
| 6. #15688979 | C2 | semidirect |
| 7. C22×C22⋊C4×C47 | C2 | semidirect |
| 11. C2×Dic47⋊C4 | C22 | semidirect |
| 16. C2×(C2×D47)⋊C4 | C22 | semidirect |
| 17. C47⋊#95 | C22 | semidirect |
| 18. C47⋊#95 | C22 | semidirect |
| 99. C22×C22⋊C4 | D47 | semidirect |
| 105. C47 | #2622 | semidirect |