Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
264 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C197 | C2×C22⋊C4 |
| commutator | C2×C4 | C22×C4×C197 |
| Frattini, cosocle | C22×C4 | C23×C197 |
| prime radical | #532×C197 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C197 ◁ C2×C42×C197 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #431×C197 | C2 | semidirect |
| 3. #382×C197 | C2 | semidirect |
| 4. #327×C197 | C2 | semidirect |
| 6. C4⋊Q8×C197 | C4 | semidirect |
| 7. #127×C197 | C4 | semidirect |
| 12. C4×D4×C197 | C4 | semidirect |
| 88. C197 | #1517 | direct (N × H) |
| 89. #1517 | C197 | direct (N × H) |
| 91. #431 | C2×C197 | semidirect |
| 92. #382 | C2×C197 | semidirect |
| 93. #327 | C2×C197 | semidirect |
| 95. C4⋊Q8 | C4×C197 | semidirect |
| 96. #127 | C4×C197 | semidirect |
| 101. C4×D4 | C4×C197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #532×C197 | 2 |
| #431×C197 | 2 |
| #382×C197 | 2 |
| #327×C197 | 2 |
| #1517 | 197 |