Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
274 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #15689038 |
| commutator | C22×C4×C47 | C23 |
| Frattini | C22×C4 | C22×D47 |
| Fitting | C47×#413 | C2 |
| socle | C2×C47 | #394 |
| hypercenter | #413 | D47 |
| hypocenter | C47 | #2048 |
| LCS | G ▷ C22×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #413 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #15689171 | C2 | semidirect |
| 3. #15689140 | C2 | semidirect |
| 4. #15689129 | C2 | semidirect |
| 5. C2×#13093940 | C2 | semidirect |
| 6. #15688894 | C2 | semidirect |
| 7. C47×#413 | C2 | semidirect |
| 115. #413 | D47 | semidirect |
| 118. C47 | #2048 | semidirect |