Finite Group DatabasebetaFinite Group DatabasebetaOrder 3008.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D188 |
| commutator, cosocle | C4×C47 | C24 |
| Frattini | C4 | C23×D47 |
| Fitting | #131×C47 | C2 |
| socle | C2×C47 | C22×D4 |
| hypercenter | #131 | D47 |
| hypocenter | C47 | #577 |
| LCS | G ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #131 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13094071 | C2 | semidirect |
| 2. #13094070 | C2 | semidirect |
| 3. #13094057 | C2 | semidirect |
| 4. #13094052 | C2 | semidirect |
| 5. #13094046 | C2 | semidirect |
| 6. C2×#10625325 | C2 | semidirect |
| 7. #131×C47 | C2 | semidirect |
| 14. #10625350 | C22 | semidirect |
| 16. C2×Dic94 | C22 | semidirect |
| 17. M16×C47 | C22 | semidirect |
| 18. C2×C8×C47 | C22 | semidirect |
| 19. Dic188 | C22 | semidirect |
| 20. D376 | C22 | semidirect |
| 21. #10625325 | C22 | semidirect |
| 22. #10625325 | C22 | semidirect |
| 23. #10625325 | C22 | semidirect |
| 54. C47 | #577 | semidirect |
| 61. #131 | D47 | semidirect |
| 76. M16 | C2×D47 | semidirect |
| 77. C2×C8 | C2×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13094071 | 2 |
| #13094070 | 2 |
| #13094057 | 2 |
| #13094052 | 2 |
| #13094046 | 2 |
| C2×#10625325 | 2 |
| #131×C47 | 2 |
| #577 | 47 |