Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
208 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 57 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. #27161431 | C2 | semidirect |
| 3. #27161286 | C2 | semidirect |
| 4. #27160827 | C2 | semidirect |
| 5. #27160809 | C2 | semidirect |
| 61. D4×C197 | Q16 | semidirect |
| 88. C197 | #1644 | semidirect |
| 144. D4 | #15691348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161786 | 2 |
| #27161431 | 2 |
| #27161286 | 2 |
| #27160827 | 2 |
| #27160809 | 2 |
| D4⋊#13096802 | 2 |
| #474×C197 | 2 |
| #1644 | 197 |