Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 3. #27161489 | C2 | semidirect |
| 4. #27161488 | C2 | semidirect |
| 5. #27161485 | C2 | semidirect |
| 6. #27161483 | C2 | semidirect |
| 7. #27161476 | C2 | semidirect |
| 11. #501×C197 | C2 | semidirect |
| 52. #15691341 | Q8 | semidirect |
| 95. #13096802 | C2×Q8 | semidirect |
| 103. C8×C197 | C2×Q8 | semidirect |
| 124. C197 | #3165 | semidirect |
| 131. #501 | D197 | semidirect |
| 228. C8 | Q8×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161635 | 2 |
| C4⋊Q8×D197 | 2 |
| #27161489 | 2 |
| #27161488 | 2 |
| #27161485 | 2 |
| #27161483 | 2 |
| #27161476 | 2 |
| #27161120 | 2 |
| #27161118 | 2 |
| #27161031 | 2 |
| #501×C197 | 2 |
| #3165 | 197 |