Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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. #27161707 | C2 | semidirect |
| 3. #27161385 | C2 | semidirect |
| 4. #27161382 | C2 | semidirect |
| 5. #27161368 | C2 | semidirect |
| 6. #27161363 | C2 | semidirect |
| 7. C2×#20263257 | C2 | semidirect |
| 8. #27161107 | C2 | semidirect |
| 11. #428×C197 | C2 | semidirect |
| 42. #15691358 | Q8 | semidirect |
| 123. C197 | #3084 | semidirect |
| 131. #428 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161707 | 2 |
| #27161560 | 2 |
| #27161385 | 2 |
| #27161382 | 2 |
| #27161368 | 2 |
| #27161363 | 2 |
| C2×#20263257 | 2 |
| #27161107 | 2 |
| #27161081 | 2 |
| #27161073 | 2 |
| #428×C197 | 2 |
| #3084 | 197 |