Finite Group DatabasebetaFinite Group DatabasebetaOrder 4288.
212 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 95 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×D67 |
| commutator, socle, cosocle | C22×C67 | C24 |
| Fitting | #126×C67 | C2 |
| prime radical | C2×C22⋊D67 | C22 |
| hypercenter | #126 | D67 |
| hypocenter | C67 | #556 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14524042 | C2 | semidirect |
| 2. #14524038 | C2 | semidirect |
| 3. #14524038 | C2 | semidirect |
| 4. #14524036 | C2 | semidirect |
| 7. #14524021 | C2 | semidirect |
| 8. #14524020 | C2 | semidirect |
| 9. C4×Dic134 | C2 | semidirect |
| 10. #14524008 | C2 | semidirect |
| 11. #14524008 | C2 | semidirect |
| 13. #14524000 | C2 | semidirect |
| 14. #14523999 | C2 | semidirect |
| 15. #126×C67 | C2 | semidirect |
| 97. C67 | #556 | semidirect |
| 103. #126 | D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14524042 | 2 |
| #14524038 | 2 |
| #14524036 | 2 |
| #14524029 | 2 |
| #14524021 | 2 |
| #14524020 | 2 |
| C4×Dic134 | 2 |
| #14524008 | 2 |
| (C22⋊D67)⋊C4 | 2 |
| #14524000 | 2 |
| #14523999 | 2 |
| #126×C67 | 2 |
| #556 | 67 |