Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
484 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 153 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. C2×#20263357 | C2 | semidirect |
| 3. #27161301 | C2 | semidirect |
| 4. #27161289 | C2 | semidirect |
| 5. #27161279 | C2 | semidirect |
| 6. #27161103 | C2 | semidirect |
| 7. #27161078 | C2 | semidirect |
| 8. C2×C4×Q8×C197 | C2 | semidirect |
| 52. C2×Q8×C197 | D4 | semidirect |
| 111. C4×C197 | #137 | semidirect |
| 120. C197 | #3037 | semidirect |
| 124. C2×C4×Q8 | D197 | semidirect |
| 160. C2×Q8 | D788 | semidirect |
| 233. C4 | #20263357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263357 | 2 |
| #27161629 | 2 |
| #27161301 | 2 |
| #27161289 | 2 |
| #27161279 | 2 |
| #27161103 | 2 |
| #27161078 | 2 |
| C2×C4×Q8×C197 | 2 |
| #3037 | 197 |