Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
1492 conjugacy classes of subgroups; only the 553 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 553 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 | C2×2−1+4×C47 | C2 |
| hypercenter | C2×2−1+4 | D47 |
| hypocenter | C47 | #3486 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C2×2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q8×D47 | C2 | semidirect |
| 2. Q8×C22⋊D47 | C2 | semidirect |
| 3. #15689780 | C2 | semidirect |
| 4. #15689694 | C2 | semidirect |
| 5. #15689630 | C2 | semidirect |
| 6. #15689601 | C2 | semidirect |
| 7. C2×2−1+4×C47 | C2 | semidirect |
| 12. #13094022 | C22 | semidirect |
| 13. #13094011 | C22 | semidirect |
| 15. #13094003 | C22 | semidirect |
| 19. Q8×Dic47 | C22 | semidirect |
| 24. C2×#41×C47 | C22 | semidirect |
| 26. C22×Q8×C47 | C22 | semidirect |
| 31. C2×Q8×C47 | D4 | semidirect |
| 78. C2×D47 | 2−1+4 | semidirect |
| 89. C2×2−1+4 | D47 | semidirect |
| 96. C47 | #3486 | semidirect |
| 99. C2×#41 | C2×D47 | semidirect |
| 104. C22×Q8 | C2×D47 | semidirect |
| 123. C2×Q8 | C22⋊D47 | semidirect |