Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 141 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. #27161429 | C2 | semidirect |
| 3. #27161412 | C2 | semidirect |
| 4. #27161374 | C2 | semidirect |
| 5. #27161318 | C2 | semidirect |
| 6. #27161286 | C2 | semidirect |
| 7. #27161235 | C2 | semidirect |
| 8. C4×#15691348 | C2 | semidirect |
| 10. C2×#20263250 | C2 | semidirect |
| 92. D4×C197 | Q16 | semidirect |
| 122. C197 | #3299 | semidirect |
| 208. D4 | #15691348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161786 | 2 |
| #27161429 | 2 |
| #27161412 | 2 |
| #27161374 | 2 |
| #27161318 | 2 |
| #27161286 | 2 |
| #27161235 | 2 |
| C4×#15691348 | 2 |
| D4×#13096802 | 2 |
| C2×#20263250 | 2 |
| D4×Q8×C197 | 2 |
| #3299 | 197 |