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. #27161749 | C2 | semidirect |
| 3. #27161442 | C2 | semidirect |
| 4. #27161425 | C2 | semidirect |
| 5. #27161381 | C2 | semidirect |
| 6. #27161370 | C2 | semidirect |
| 7. #27161272 | C2 | semidirect |
| 8. #27161206 | C2 | semidirect |
| 9. #27161191 | C2 | semidirect |
| 10. C4×#15691343 | C2 | semidirect |
| 11. #459×C197 | C2 | semidirect |
| 97. D4×C197 | #41 | semidirect |
| 129. C197 | #3366 | semidirect |
| 138. #459 | D197 | semidirect |
| 218. D4 | #15691357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161786 | 2 |
| #27161749 | 2 |
| #27161442 | 2 |
| #27161425 | 2 |
| #27161381 | 2 |
| #27161370 | 2 |
| #27161272 | 2 |
| #27161206 | 2 |
| #27161191 | 2 |
| C4×#15691343 | 2 |
| #459×C197 | 2 |
| #3366 | 197 |