Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
246 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 100 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 | C42 | C23×C197 |
| socle | C22×C197 | C2×C22⋊C4 |
| prime radical | C2×#41×C197 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C197 ◁ C2×C42×C197 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #432×C197 | C2 | semidirect |
| 3. #431×C197 | C2 | semidirect |
| 4. Q8⋊C8×C197 | C2 | semidirect |
| 5. D4⋊C8×C197 | C2 | semidirect |
| 97. C197 | #1488 | direct (N × H) |
| 98. #1488 | C197 | direct (N × H) |
| 100. #432 | C2×C197 | semidirect |
| 101. #431 | C2×C197 | semidirect |
| 102. Q8⋊C8 | C2×C197 | semidirect |
| 103. D4⋊C8 | C2×C197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#41×C197 | 2 |
| #432×C197 | 2 |
| #431×C197 | 2 |
| Q8⋊C8×C197 | 2 |
| D4⋊C8×C197 | 2 |
| #1488 | 197 |