Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D197 | C2 | semidirect |
| 3. #27161373 | C2 | semidirect |
| 4. #27161367 | C2 | semidirect |
| 5. #27161365 | C2 | semidirect |
| 6. #27161361 | C2 | semidirect |
| 7. #27161359 | C2 | semidirect |
| 8. #27161120 | C2 | semidirect |
| 9. #27161101 | C2 | semidirect |
| 11. #474×C197 | C2 | semidirect |
| 44. #15691357 | Q8 | semidirect |
| 86. Dic394 | C2×Q8 | semidirect |
| 105. D4×C197 | C2×Q8 | semidirect |
| 137. C197 | #3079 | semidirect |
| 146. #474 | D197 | semidirect |
| 229. D4 | Q8×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D197 | 2 |
| C4×#15691357 | 2 |
| #27161373 | 2 |
| #27161367 | 2 |
| #27161365 | 2 |
| #27161361 | 2 |
| #27161359 | 2 |
| #27161120 | 2 |
| #27161101 | 2 |
| #27161077 | 2 |
| #474×C197 | 2 |
| #3079 | 197 |