Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
306 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C197 | C2×D4 |
| commutator | C2×C4 | C22×C4×C197 |
| Frattini, cosocle | C22×C4 | C23×C197 |
| socle | C22×C197 | C2×C22⋊C4 |
| prime radical | C24×C197 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C197 ◁ C23×C4×C197 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #339×C197 | C2 | semidirect |
| 9. #117×C197 | C4 | semidirect |
| 11. C2×C4⋊C4×C197 | C4 | semidirect |
| 12. C2×C4⋊C4×C197 | C4 | semidirect |
| 91. C197 | #1826 | direct (N × H) |
| 92. #1826 | C197 | direct (N × H) |
| 96. #339 | C2×C197 | semidirect |
| 101. #117 | C4×C197 | semidirect |
| 103. C2×C4⋊C4 | C4×C197 | semidirect |
| 104. C2×C4⋊C4 | C4×C197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#117×C197 | 2 |
| #407×C197 | 2 |
| C4×C22⋊C4×C197 | 2 |
| #339×C197 | 2 |
| #1826 | 197 |