Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
278 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 278 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 | #13093992 |
| commutator | C42×C47 | C23 |
| Frattini | C42 | C22×D47 |
| Fitting | C47×#460 | C2 |
| socle | C22×C47 | #120 |
| hypercenter | #460 | D47 |
| hypocenter | C47 | #1621 |
| LCS | G ▷ C42×C47 ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #460 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15689795 | C2 | semidirect |
| 2. #15689499 | C2 | semidirect |
| 3. #15689315 | C2 | semidirect |
| 4. #15688866 | C2 | semidirect |
| 5. Q8⋊(C47⋊C8) | C2 | semidirect |
| 6. #15688850 | C2 | semidirect |
| 7. C47×#460 | C2 | semidirect |
| 56. Q8×C47 | D8 | semidirect |
| 110. #460 | D47 | semidirect |
| 115. C47 | #1621 | semidirect |
| 164. Q8 | #10625334 | semidirect |