Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
172 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #13093998 |
| commutator | C42×C47 | C23 |
| Frattini | C42 | C22×D47 |
| Fitting | C8×Q8×C47 | C2 |
| socle | C22×C47 | #121 |
| hypercenter | C8×Q8 | D47 |
| hypocenter | C47 | #1666 |
| LCS | G ▷ C42×C47 ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ C8×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #15689408 | C2 | semidirect |
| 4. #15688874 | C2 | semidirect |
| 5. #15688870 | C2 | semidirect |
| 7. C8×Q8×C47 | C2 | semidirect |
| 44. Q8×C47 | SD16 | semidirect |
| 60. C8×C47 | SD16 | semidirect |
| 83. C8×Q8 | D47 | semidirect |
| 87. C47 | #1666 | semidirect |
| 126. Q8 | #10625325 | semidirect |
| 142. C8 | #10625336 | semidirect |