Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
432 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 107 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. C22×C8×D197 | C2 | semidirect |
| 3. C2×#20263248 | C2 | semidirect |
| 4. C2×#20263246 | C2 | semidirect |
| 5. #27160936 | C2 | semidirect |
| 6. #27160841 | C2 | semidirect |
| 7. #340×C197 | C2 | semidirect |
| 16. #20263301 | C4 | semidirect |
| 47. C2×#13096802 | D4 | semidirect |
| 58. C2×C8×C197 | D4 | semidirect |
| 127. C2×D197 | #102 | semidirect |
| 145. C197 | #1893 | semidirect |
| 153. #340 | D197 | semidirect |
| 200. C2×C8 | D788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D197 | 2 |
| C2×#20263301 | 2 |
| C2×#20263248 | 2 |
| C2×#20263246 | 2 |
| #27160936 | 2 |
| #27160841 | 2 |
| #340×C197 | 2 |
| #1893 | 197 |