Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
360 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 2. C2×#20263258 | C2 | semidirect |
| 3. C2×#20263257 | C2 | semidirect |
| 6. #27160841 | C2 | semidirect |
| 7. #340×C197 | C2 | semidirect |
| 19. #20263238 | C4 | semidirect |
| 39. C2×#13096802 | C2×C4 | semidirect |
| 51. C2×C8×C197 | C2×C4 | semidirect |
| 105. C2×D197 | #106 | semidirect |
| 123. C197 | #1853 | semidirect |
| 131. #340 | D197 | semidirect |
| 169. C2×C8 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×D197 | 2 |
| C2×#20263258 | 2 |
| C2×#20263257 | 2 |
| C2×#20263238 | 2 |
| #27160936 | 2 |
| #27160841 | 2 |
| #340×C197 | 2 |
| #1853 | 197 |