Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
276 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 75 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. #27161101 | C2 | semidirect |
| 3. C4×C8×D197 | C2 | semidirect |
| 4. #27160808 | C2 | semidirect |
| 5. D4⋊#13096802 | C2 | semidirect |
| 6. #27160806 | C2 | semidirect |
| 7. D4⋊C8×C197 | C2 | semidirect |
| 117. C197 | #1492 | semidirect |
| 125. D4⋊C8 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161626 | 2 |
| #27161101 | 2 |
| C4×C8×D197 | 2 |
| #27160808 | 2 |
| D4⋊#13096802 | 2 |
| #27160806 | 2 |
| D4⋊C8×C197 | 2 |
| #1492 | 197 |