Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
388 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 195 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. #27161209 | C2 | semidirect |
| 3. #27161206 | C2 | semidirect |
| 4. Q8×#13096802 | C2 | semidirect |
| 7. C8×Q8×C197 | C2 | semidirect |
| 30. #15691341 | Q8 | direct (N × H) |
| 53. #13096802 | C2×Q8 | semidirect |
| 54. Q8×C197 | M16 | semidirect |
| 59. C8×C197 | C2×Q8 | semidirect |
| 75. C197 | Q8×M16 | semidirect |
| 81. C8×Q8 | D197 | semidirect |
| 121. Q8 | #15691341 | direct (N × H) |
| 135. C8 | Q8×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×D197 | 2 |
| #27161209 | 2 |
| #27161206 | 2 |
| Q8×#13096802 | 2 |
| #27161101 | 2 |
| C4×#15691341 | 2 |
| C8×Q8×C197 | 2 |
| Q8×M16 | 197 |