Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
392 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 139 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×Dic394 | C2 | semidirect |
| 2. #27161425 | C2 | semidirect |
| 3. #27161369 | C2 | semidirect |
| 4. #27161276 | C2 | semidirect |
| 5. Q8×#13096802 | C2 | semidirect |
| 6. C4×#15691346 | C2 | semidirect |
| 45. Dic394 | #41 | semidirect |
| 51. Q8×C197 | SD16 | semidirect |
| 76. C197 | #3362 | semidirect |
| 124. Q8 | #15691346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic394 | 2 |
| #27161425 | 2 |
| #27161369 | 2 |
| #27161276 | 2 |
| Q8×#13096802 | 2 |
| C4×#15691346 | 2 |
| #550×C197 | 2 |
| #3362 | 197 |