Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. C4×#15691342 | C2 | semidirect |
| 3. C42×Dic197 | C2 | semidirect |
| 4. #27160838 | C2 | semidirect |
| 9. #20263253 | C4 | direct (N × H) |
| 13. C4×Q8×C197 | C4 | semidirect |
| 15. C4×D4×C197 | C4 | semidirect |
| 22. #15691342 | C2×C4 | semidirect |
| 26. C4×Dic197 | C2×C4 | semidirect |
| 51. Q8×C197 | C42 | semidirect |
| 54. D4×C197 | C42 | semidirect |
| 74. C4×C197 | #104 | semidirect |
| 83. C197 | C4×#104 | semidirect |
| 92. C4×Q8 | Dic197 | semidirect |
| 94. C4×D4 | Dic197 | semidirect |
| 132. Q8 | C4×Dic197 | semidirect |
| 135. D4 | C4×Dic197 | semidirect |
| 159. C4 | #20263253 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263253 | 2 |
| C4×#15691342 | 2 |
| C42×Dic197 | 2 |
| #27160838 | 2 |
| C4×#41×C197 | 2 |
| C4×#104 | 197 |