Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
346 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #15688999 |
| commutator | C2×C4×C47 | C22×C4 |
| Frattini | C22×C4 | C22×D47 |
| Fitting | C47×#410 | C2 |
| socle | C2×C47 | #386 |
| hypercenter | #410 | D47 |
| hypocenter | C47 | #1904 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #410 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #15689597 | C2 | semidirect |
| 3. #15689140 | C2 | semidirect |
| 4. #15689127 | C2 | semidirect |
| 5. #15688893 | C2 | semidirect |
| 6. #15688879 | C2 | semidirect |
| 7. C47×#410 | C2 | semidirect |
| 11. C2×#10625336 | C4 | semidirect |
| 12. C2×#10625334 | C4 | semidirect |
| 30. C2×Q8×C47 | C2×C4 | semidirect |
| 32. C2×D4×C47 | C2×C4 | semidirect |
| 59. C2×C47⋊C8 | C2×C4 | semidirect |
| 120. #410 | D47 | semidirect |
| 123. C47 | #1904 | semidirect |
| 146. C2×Q8 | C4×D47 | semidirect |
| 154. C2×D4 | C4×D47 | semidirect |