Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
496 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 496 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×D197 |
| commutator | C22×C197 | C23×C4 |
| Fitting | #391×C197 | C2 |
| socle, prime radical, cosocle | C23×C197 | C24 |
| hypercenter | #391 | D197 |
| hypocenter | C197 | #2369 |
| LCS | G ▷ C22×C197 ▷ C197 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. #20263324 | C4 | semidirect |
| 44. #15691337 | Q8 | semidirect |
| 109. C197 | #2369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263324 | 2 |
| #27160986 | 2 |
| #27160983 | 2 |
| #27160976 | 2 |
| #27160974 | 2 |
| C4×#15691337 | 2 |
| #27160930 | 2 |
| #391×C197 | 2 |
| #2369 | 197 |