Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
612 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 3. #27160986 | C2 | semidirect |
| 5. #27160970 | C2 | semidirect |
| 6. #27160950 | C2 | semidirect |
| 7. #27160948 | C2 | semidirect |
| 8. #27160925 | C2 | semidirect |
| 9. C2×C4×Q8×C197 | C2 | semidirect |
| 12. #20263315 | C4 | semidirect |
| 43. #15691335 | C2×C4 | semidirect |
| 45. C4×Dic197 | C2×C4 | semidirect |
| 48. C2×Q8×C197 | C2×C4 | semidirect |
| 111. C197 | #2326 | semidirect |
| 114. C2×C4×Q8 | D197 | semidirect |
| 145. C2×Q8 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263315 | 2 |
| C2×C4×D788 | 2 |
| #27160986 | 2 |
| #27160980 | 2 |
| #27160970 | 2 |
| #27160950 | 2 |
| #27160948 | 2 |
| #27160925 | 2 |
| C2×C4×Q8×C197 | 2 |
| #2326 | 197 |