Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 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 |
|---|---|---|
| 1. #27161786 | C2 | semidirect |
| 2. #27161750 | C2 | semidirect |
| 3. #27161442 | C2 | semidirect |
| 4. #27161426 | C2 | semidirect |
| 5. #27161382 | C2 | semidirect |
| 6. #27161369 | C2 | semidirect |
| 7. #27161274 | C2 | semidirect |
| 8. #27161272 | C2 | semidirect |
| 9. #27161209 | C2 | semidirect |
| 10. #27161188 | C2 | semidirect |
| 11. C4×D8×C197 | C2 | semidirect |
| 94. D4×C197 | #41 | semidirect |
| 129. C197 | #3366 | semidirect |
| 141. C4×D8 | D197 | semidirect |
| 218. D4 | #15691358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161786 | 2 |
| #27161750 | 2 |
| #27161442 | 2 |
| #27161426 | 2 |
| #27161382 | 2 |
| #27161369 | 2 |
| #27161274 | 2 |
| #27161272 | 2 |
| #27161209 | 2 |
| #27161188 | 2 |
| C4×D8×C197 | 2 |
| #3366 | 197 |