Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
336 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #13093992 |
| commutator | C42×C47 | C23 |
| Frattini | C42 | C22×D47 |
| Fitting | C47×#459 | C2 |
| socle | C22×C47 | #120 |
| hypercenter | #459 | D47 |
| hypocenter | C47 | #1619 |
| LCS | G ▷ C42×C47 ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #459 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D4×D188 | C2 | semidirect |
| 2. #15689499 | C2 | semidirect |
| 3. #15689315 | C2 | semidirect |
| 4. #15688866 | C2 | semidirect |
| 5. D4⋊(C47⋊C8) | C2 | semidirect |
| 6. #15688850 | C2 | semidirect |
| 7. C47×#459 | C2 | semidirect |
| 17. C4⋊(C47⋊C8) | C22 | semidirect |
| 19. C4×C47⋊C8 | C22 | semidirect |
| 21. #127×C47 | C22 | semidirect |
| 23. C4⋊C8×C47 | C22 | semidirect |
| 67. D4×C47 | D8 | semidirect |
| 83. D188 | D8 | semidirect |
| 121. #459 | D47 | semidirect |
| 125. C47 | #1619 | semidirect |
| 132. #127 | C2×D47 | semidirect |
| 139. C4⋊C8 | C2×D47 | semidirect |
| 194. D4 | #10625334 | semidirect |