Finite Group DatabasebetaFinite Group DatabasebetaOrder 14656.
252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 252 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×D229 |
| commutator, socle, cosocle | C22×C229 | C24 |
| Fitting | #120×C229 | C2 |
| hypercenter | #120 | D229 |
| hypocenter | C229 | #560 |
| LCS | G ▷ C22×C229 ▷ C229 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20300984 | C2 | semidirect |
| 2. #20300981 | C2 | semidirect |
| 3. #20300970 | C2 | semidirect |
| 4. #20300969 | C2 | semidirect |
| 5. #20300961 | C2 | semidirect |
| 6. #20300960 | C2 | semidirect |
| 7. #20300959 | C2 | semidirect |
| 8. #20300957 | C2 | semidirect |
| 9. #120×C229 | C2 | semidirect |
| 10. C2×D916 | C22 | semidirect |
| 14. C2×C22⋊D229 | C22 | semidirect |
| 15. C22×Dic229 | C22 | semidirect |
| 16. C2×C4×D229 | C22 | semidirect |
| 17. C4⋊Dic229 | C22 | semidirect |
| 18. #16814645 | C22 | semidirect |
| 19. #16814645 | C22 | semidirect |
| 23. C22⋊Dic229 | C22 | semidirect |
| 24. #16814643 | C22 | semidirect |
| 25. C4×Dic229 | C22 | semidirect |
| 74. C229 | #560 | semidirect |
| 84. #120 | D229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20300984 | 2 |
| #20300981 | 2 |
| #20300970 | 2 |
| #20300969 | 2 |
| #20300961 | 2 |
| #20300960 | 2 |
| #20300959 | 2 |
| #20300957 | 2 |
| #120×C229 | 2 |
| #560 | 229 |