Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
180 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 89 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. Q8×#13096802 | C2 | semidirect |
| 3. #27160830 | C2 | semidirect |
| 4. Q8⋊#13096802 | C2 | semidirect |
| 6. C8×#13096802 | C2 | semidirect |
| 32. SD16×C197 | C8 | semidirect |
| 45. #13096802 | SD16 | direct (N × H) |
| 48. Q8×C197 | C2×C8 | semidirect |
| 60. C8×C197 | C2×C8 | semidirect |
| 77. C197 | C8×SD16 | semidirect |
| 104. SD16 | #13096802 | direct (N × H) |
| 121. Q8 | C2×#13096802 | semidirect |
| 138. C8 | C2×#13096802 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#13096802 | 2 |
| D4×#13096802 | 2 |
| #27160830 | 2 |
| Q8⋊#13096802 | 2 |
| D4⋊#13096802 | 2 |
| C8×#13096802 | 2 |
| C4×SD16×C197 | 2 |
| C8×SD16 | 197 |