Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
424 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 173 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 | C22×C227 | C23×C4 |
| Fitting | #391×C227 | C2 |
| socle, prime radical, cosocle | C23×C227 | C24 |
| hypercenter | #391 | D227 |
| hypocenter | C227 | #2381 |
| LCS | G ▷ C22×C227 ▷ C227 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. #20300286 | C4 | semidirect |
| 103. C227 | #2381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300286 | 2 |
| #28408939 | 2 |
| #28408936 | 2 |
| #28408919 | 2 |
| #28408916 | 2 |
| #28408914 | 2 |
| #28408913 | 2 |
| #28408899 | 2 |
| #391×C227 | 2 |
| #2381 | 227 |