Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
402 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D47 |
| commutator, socle | C22×C47 | C23×C4 |
| Fitting | C47×#525 | C2 |
| hypercenter | #525 | D47 |
| hypocenter | C47 | #2978 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C4 ◁ #525 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15689201 | C2 | semidirect |
| 2. #15689195 | C2 | semidirect |
| 3. #15689184 | C2 | semidirect |
| 4. #15689090 | C2 | semidirect |
| 5. #15689087 | C2 | semidirect |
| 8. C2×#10625329 | C22 | semidirect |
| 9. C22×C47⋊C8 | C22 | semidirect |
| 10. C4⋊(C47⋊C8) | C22 | semidirect |
| 14. C22⋊(C47⋊C8) | C22 | semidirect |
| 15. #13093935 | C22 | semidirect |
| 16. C4×C47⋊C8 | C22 | semidirect |
| 96. C47 | #2978 | semidirect |