Finite Group DatabasebetaFinite Group DatabasebetaOrder 3008.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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 | C2×C22⋊D47 | C22 |
| hypercenter | #126 | D47 |
| hypocenter | C47 | #563 |
| 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. #13094024 | C2 | semidirect |
| 2. #13094023 | C2 | semidirect |
| 3. #13094019 | C2 | semidirect |
| 4. #13094018 | C2 | semidirect |
| 5. #13094017 | C2 | semidirect |
| 6. #13094015 | C2 | semidirect |
| 7. #13094014 | C2 | semidirect |
| 11. #13094004 | C2 | semidirect |
| 12. #13094002 | C2 | semidirect |
| 13. #13094001 | C2 | semidirect |
| 14. #13094001 | C2 | semidirect |
| 15. #126×C47 | C2 | semidirect |
| 98. C47 | #563 | semidirect |
| 104. #126 | D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13094024 | 2 |
| #13094023 | 2 |
| #13094019 | 2 |
| #13094018 | 2 |
| #13094017 | 2 |
| #13094015 | 2 |
| #13094014 | 2 |
| #13094010 | 2 |
| #13094008 | 2 |
| #13094006 | 2 |
| #13094004 | 2 |
| #13094002 | 2 |
| #13094001 | 2 |
| #126×C47 | 2 |
| #563 | 47 |