Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
1068 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 209 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D227 |
| commutator, socle, cosocle | C23×C227 | C24 |
| Fitting | #379×C227 | C2 |
| prime radical | C25×C227 | C22 |
| hypercenter | #379 | D227 |
| hypocenter | C227 | #2848 |
| LCS | G ▷ C23×C227 ▷ C227 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#20300265 | C2 | semidirect |
| 3. #28408907 | C2 | semidirect |
| 4. #28408904 | C2 | semidirect |
| 5. #28408890 | C2 | semidirect |
| 8. C22×Dic454 | C22 | semidirect |
| 13. C2×C4⋊Dic227 | C22 | semidirect |
| 14. C2×Dic227⋊C4 | C22 | semidirect |
| 15. C2×Dic227⋊C4 | C22 | semidirect |
| 18. C227⋊#95 | C22 | semidirect |
| 39. C24×C227 | Q8 | semidirect |
| 71. C22×C227 | C22⋊Q8 | semidirect |
| 85. C227 | #2848 | semidirect |
| 110. C24 | Dic454 | semidirect |
| 157. C22 | #20300265 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic227 | 2 |
| C2×#20300265 | 2 |
| #28408907 | 2 |
| #28408904 | 2 |
| #28408890 | 2 |
| #28408888 | 2 |
| #379×C227 | 2 |
| #2848 | 227 |