Finite Group DatabasebetaFinite Group DatabasebetaOrder 3008.
234 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D47 |
| commutator, socle, cosocle | C22×C47 | C24 |
| Fitting | #126×C47 | C2 |
| prime radical | #13093997 | C2 |
| hypercenter | #126 | D47 |
| hypocenter | C47 | #529 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13094018 | C2 | semidirect |
| 2. #13094014 | C2 | semidirect |
| 3. #13094010 | C2 | semidirect |
| 4. #13094009 | C2 | semidirect |
| 5. #13094006 | C2 | semidirect |
| 6. #13094002 | C2 | semidirect |
| 8. #13093989 | C2 | semidirect |
| 9. #13093986 | C2 | semidirect |
| 10. (C22⋊D47)⋊C4 | C2 | semidirect |
| 11. (C22⋊D47)⋊C4 | C2 | semidirect |
| 12. #13093982 | C2 | semidirect |
| 13. #13093980 | C2 | semidirect |
| 14. C42×D47 | C2 | semidirect |
| 15. #126×C47 | C2 | semidirect |
| 104. C47 | #529 | semidirect |
| 106. #126 | D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13094018 | 2 |
| #13094014 | 2 |
| #13094010 | 2 |
| #13094009 | 2 |
| #13094006 | 2 |
| #13094002 | 2 |
| #13093997 | 2 |
| #13093989 | 2 |
| #13093986 | 2 |
| (C22⋊D47)⋊C4 | 2 |
| #13093982 | 2 |
| #13093980 | 2 |
| C42×D47 | 2 |
| #126×C47 | 2 |
| #529 | 47 |