Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
344 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 344 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, socle | C2×C197 | #386 |
| commutator | C2×C4 | C22×C4×C197 |
| Frattini, cosocle | C22×C4 | C23×C197 |
| prime radical | #535×C197 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C197 ◁ C22×C4×C197 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #568×C197 | C2 | semidirect |
| 3. #418×C197 | C2 | semidirect |
| 4. #410×C197 | C2 | semidirect |
| 5. H(3,ℤ/4)×C197 | C2 | semidirect |
| 11. #127×C197 | C4 | semidirect |
| 12. #124×C197 | C4 | semidirect |
| 36. C2×C8×C197 | D4 | semidirect |
| 85. C197 | #1910 | direct (N × H) |
| 86. #1910 | C197 | direct (N × H) |
| 87. #568 | C2×C197 | semidirect |
| 89. #418 | C2×C197 | semidirect |
| 90. #410 | C2×C197 | semidirect |
| 91. H(3,ℤ/4) | C2×C197 | semidirect |
| 97. #127 | C4×C197 | semidirect |
| 98. #124 | C4×C197 | semidirect |
| 122. C2×C8 | D4×C197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #568×C197 | 2 |
| #535×C197 | 2 |
| #418×C197 | 2 |
| #410×C197 | 2 |
| H(3,ℤ/4)×C197 | 2 |
| #1910 | 197 |