Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
204 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #13093996 |
| commutator | C42×C47 | C23 |
| Frattini | C42 | C22×D47 |
| Fitting | C47×#459 | C2 |
| socle | C22×C47 | #121 |
| hypercenter | #459 | D47 |
| hypocenter | C47 | #1667 |
| 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. #15689499 | C2 | semidirect |
| 2. #15689318 | C2 | semidirect |
| 3. D4×C47⋊C8 | C2 | semidirect |
| 4. #15688875 | C2 | semidirect |
| 5. #15688867 | C2 | semidirect |
| 6. #15688866 | C2 | semidirect |
| 7. C47×#459 | C2 | semidirect |
| 53. D4×C47 | D8 | semidirect |
| 69. C47⋊C8 | D8 | semidirect |
| 95. #459 | D47 | semidirect |
| 100. C47 | #1667 | semidirect |
| 151. D4 | #10625334 | semidirect |