Finite Group DatabasebetaFinite Group DatabasebetaOrder 25408.
124 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 53 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. C2×#20263714 | C2 | semidirect |
| 2. C2×C8×D397 | C2 | semidirect |
| 4. C4⋊#15691787 | C2 | semidirect |
| 5. #27163008 | C2 | semidirect |
| 6. #27163008 | C2 | semidirect |
| 7. #97×C397 | C2 | semidirect |
| 36. C8×C397 | D4 | semidirect |
| 43. C2×D397 | M16 | semidirect |
| 55. C397 | #435 | semidirect |
| 63. #97 | D397 | semidirect |
| 92. C8 | D1588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263714 | 2 |
| C2×C8×D397 | 2 |
| C4×D1588 | 2 |
| C4⋊#15691787 | 2 |
| #27163008 | 2 |
| #97×C397 | 2 |
| #435 | 397 |