Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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. #27161371 | C2 | semidirect |
| 3. #27161366 | C2 | semidirect |
| 4. #27161361 | C2 | semidirect |
| 5. #27161356 | C2 | semidirect |
| 6. #27161119 | C2 | semidirect |
| 7. #27161103 | C2 | semidirect |
| 9. C2×C4⋊Q8×C197 | C2 | semidirect |
| 36. #15691358 | Q8 | semidirect |
| 72. Dic394 | C2×Q8 | semidirect |
| 74. D788 | C2×Q8 | semidirect |
| 121. C197 | #3079 | semidirect |
| 123. C2×C4⋊Q8 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15691358 | 2 |
| #27161371 | 2 |
| #27161366 | 2 |
| #27161361 | 2 |
| #27161356 | 2 |
| #27161119 | 2 |
| #27161103 | 2 |
| #27161078 | 2 |
| C2×C4⋊Q8×C197 | 2 |
| #3079 | 197 |