Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D188 |
| commutator | C2×C4×C47 | C24 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#443 | C2 |
| socle | C2×C47 | D42 |
| hypercenter | #443 | D47 |
| hypocenter | C47 | #3293 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #443 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15689940 | C2 | semidirect |
| 2. #15689937 | C2 | semidirect |
| 3. #15689503 | C2 | semidirect |
| 4. #15689399 | C2 | semidirect |
| 5. #15689398 | C2 | semidirect |
| 6. #15689307 | C2 | semidirect |
| 7. #15689241 | C2 | semidirect |
| 8. C47×#443 | C2 | semidirect |
| 107. #443 | D47 | semidirect |
| 108. C47 | #3293 | semidirect |