Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#20263255 | C2 | semidirect |
| 4. #27160948 | C2 | semidirect |
| 5. #27160842 | C2 | semidirect |
| 6. #27160841 | C2 | semidirect |
| 11. D4×Dic197 | C4 | semidirect |
| 82. D4×C197 | C4⋊C4 | semidirect |
| 115. Dic197 | #102 | semidirect |
| 124. C197 | #1802 | semidirect |
| 193. D4 | #15691337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic197 | 2 |
| C2×#20263255 | 2 |
| C2×#20263247 | 2 |
| #27160948 | 2 |
| #27160842 | 2 |
| #27160841 | 2 |
| C2×#102×C197 | 2 |
| #1802 | 197 |