Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
180 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 65 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. #27161156 | C2 | semidirect |
| 3. #27160806 | C2 | semidirect |
| 4. C8×#13096802 | C2 | semidirect |
| 5. #335×C197 | C2 | semidirect |
| 37. #13096802 | D8 | semidirect |
| 43. C8×C197 | M16 | semidirect |
| 58. C197 | #1589 | semidirect |
| 62. #335 | D197 | semidirect |
| 102. C8 | #15691341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D1576 | 2 |
| #27161156 | 2 |
| #27160806 | 2 |
| C8×#13096802 | 2 |
| #335×C197 | 2 |
| #1589 | 197 |