Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
442 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C4×Dic197 | C2 | semidirect |
| 2. C2×#20263253 | C2 | semidirect |
| 3. #27161043 | C2 | semidirect |
| 4. #27160838 | C2 | semidirect |
| 16. C22⋊Q8×C197 | C4 | semidirect |
| 17. #121×C197 | C4 | semidirect |
| 29. C4×Dic197 | D4 | semidirect |
| 33. C2×Q8×C197 | C2×C4 | semidirect |
| 36. C2×D4×C197 | C2×C4 | semidirect |
| 45. C4⋊C4×C197 | C2×C4 | semidirect |
| 84. C22×C197 | #104 | semidirect |
| 100. C197 | #1896 | semidirect |
| 112. C22⋊Q8 | Dic197 | semidirect |
| 113. #121 | Dic197 | semidirect |
| 125. C2×Q8 | C2×Dic197 | semidirect |
| 128. C2×D4 | C2×Dic197 | semidirect |
| 143. C4⋊C4 | C2×Dic197 | semidirect |
| 185. C22 | #20263253 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic197 | 2 |
| C2×#20263253 | 2 |
| #27161043 | 2 |
| #27160838 | 2 |
| #525×C197 | 2 |
| #1896 | 197 |