Finite Group DatabasebetaFinite Group DatabasebetaOrder 25408.
294 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 151 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. C4×Dic794 | C2 | semidirect |
| 3. C4×D1588 | C2 | semidirect |
| 4. #27163056 | C2 | semidirect |
| 5. #27163054 | C2 | semidirect |
| 6. C2×C4⋊Dic397 | C2 | semidirect |
| 7. C4⋊C4×D397 | C2 | semidirect |
| 8. #117×C397 | C2 | semidirect |
| 9. #20263731 | C4 | semidirect |
| 27. Dic794 | C2×C4 | semidirect |
| 28. D1588 | C2×C4 | semidirect |
| 29. C22⋊D397 | C2×C4 | semidirect |
| 34. C4×D397 | C2×C4 | semidirect |
| 36. C2×C4×C397 | C2×C4 | semidirect |
| 59. C397 | #520 | semidirect |
| 66. #117 | D397 | semidirect |
| 96. C2×C4 | C4×D397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263731 | 2 |
| C4×Dic794 | 2 |
| C4×D1588 | 2 |
| #27163056 | 2 |
| #27163054 | 2 |
| C2×C4⋊Dic397 | 2 |
| C4⋊C4×D397 | 2 |
| #117×C397 | 2 |
| #520 | 397 |