Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
332 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 97 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×C22⋊#13096802 | C2 | semidirect |
| 3. #27160804 | C2 | semidirect |
| 4. #27160802 | C2 | semidirect |
| 5. C2×C22⋊C8×C197 | C2 | semidirect |
| 27. C2×C22⋊D197 | C8 | semidirect |
| 58. C22×D197 | C2×C8 | semidirect |
| 67. C2×Dic197 | C2×C8 | semidirect |
| 122. C197 | #1459 | semidirect |
| 126. C2×C22⋊C8 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D197 | 2 |
| C2×C22⋊#13096802 | 2 |
| #27160804 | 2 |
| #27160802 | 2 |
| C2×C22⋊C8×C197 | 2 |
| #1459 | 197 |