Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
368 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 145 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. #27161482 | C2 | semidirect |
| 3. #27161458 | C2 | semidirect |
| 4. #27161431 | C2 | semidirect |
| 5. #27161429 | C2 | semidirect |
| 7. C4×#15691348 | C2 | semidirect |
| 79. C2×C4×C197 | Q16 | semidirect |
| 104. C197 | #3170 | semidirect |
| 182. C2×C4 | #15691348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161636 | 2 |
| #27161482 | 2 |
| #27161458 | 2 |
| #27161431 | 2 |
| #27161429 | 2 |
| #27161318 | 2 |
| C4×#15691348 | 2 |
| C2×C4×#13096802 | 2 |
| #533×C197 | 2 |
| #3170 | 197 |