Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
652 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 213 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 | C22×C47 | C23×C4 |
| Fitting | C47×#391 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | #391 | D47 |
| hypocenter | C47 | C4×#124 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×Q8×Dic47 | C2 | semidirect |
| 5. #15689015 | C2 | semidirect |
| 6. #15688988 | C2 | semidirect |
| 7. #15688970 | C2 | semidirect |
| 8. C42×Dic47 | C2 | semidirect |
| 9. C47×#391 | C2 | semidirect |
| 12. #13094013 | C4 | semidirect |
| 33. C2×Q8×C47 | C2×C4 | semidirect |
| 51. (C2×D47)⋊C4 | C2×C4 | semidirect |
| 57. C4×Dic47 | C2×C4 | semidirect |
| 105. Dic47 | #124 | semidirect |
| 116. #391 | D47 | semidirect |
| 122. C47 | C4×#124 | semidirect |
| 146. C2×Q8 | C4×D47 | semidirect |