Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
568 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 161 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. #27161018 | C2 | semidirect |
| 3. #27161005 | C2 | semidirect |
| 5. #27160990 | C2 | semidirect |
| 6. C4×#15691335 | C2 | semidirect |
| 7. #27160925 | C2 | semidirect |
| 8. C2×C4×Q8×C197 | C2 | semidirect |
| 96. C197 | #2398 | semidirect |
| 98. C2×C4×Q8 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D788 | 2 |
| #27161018 | 2 |
| #27161005 | 2 |
| #27160996 | 2 |
| #27160990 | 2 |
| C4×#15691335 | 2 |
| #27160925 | 2 |
| C2×C4×Q8×C197 | 2 |
| #2398 | 197 |