Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
376 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 3. #27161388 | C2 | semidirect |
| 4. #27161384 | C2 | semidirect |
| 5. #27161372 | C2 | semidirect |
| 6. #27161362 | C2 | semidirect |
| 72. C2×Q8×C197 | Q8 | semidirect |
| 129. C197 | #3078 | semidirect |
| 177. C2×Q8 | Dic394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161632 | 2 |
| C2×Q8×Dic197 | 2 |
| #27161388 | 2 |
| #27161384 | 2 |
| #27161372 | 2 |
| #27161362 | 2 |
| #27161122 | 2 |
| #27161121 | 2 |
| #27161102 | 2 |
| #27161088 | 2 |
| #419×C197 | 2 |
| #3078 | 197 |