Finite Group DatabasebetaFinite Group DatabasebetaOrder 3776.
218 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 93 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×D59 |
| commutator, socle, cosocle | C22×C59 | C24 |
| Fitting | C22⋊Q8×C59 | C2 |
| prime radical | #14273700 | C2 |
| hypercenter | C22⋊Q8 | D59 |
| hypocenter | C59 | #539 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14273722 | C2 | semidirect |
| 2. #14273720 | C2 | semidirect |
| 3. #14273717 | C2 | semidirect |
| 4. #14273717 | C2 | semidirect |
| 5. #14273712 | C2 | semidirect |
| 6. #14273710 | C2 | semidirect |
| 7. #14273709 | C2 | semidirect |
| 8. #14273709 | C2 | semidirect |
| 9. #14273703 | C2 | semidirect |
| 10. #14273703 | C2 | semidirect |
| 12. #14273689 | C2 | semidirect |
| 13. C4×C22⋊D59 | C2 | semidirect |
| 14. C4⋊C4×D59 | C2 | semidirect |
| 15. C22⋊Q8×C59 | C2 | semidirect |
| 104. C59 | #539 | semidirect |
| 115. C22⋊Q8 | D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14273722 | 2 |
| #14273720 | 2 |
| #14273717 | 2 |
| #14273712 | 2 |
| #14273710 | 2 |
| #14273709 | 2 |
| #14273703 | 2 |
| #14273700 | 2 |
| #14273689 | 2 |
| C4×C22⋊D59 | 2 |
| C4⋊C4×D59 | 2 |
| C22⋊Q8×C59 | 2 |
| #539 | 59 |