Finite Group DatabasebetaFinite Group DatabasebetaOrder 25408.
144 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 43 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×#20263718 | C2 | semidirect |
| 2. C2×D3176 | C2 | semidirect |
| 3. C2×#20263716 | C2 | semidirect |
| 4. #27163092 | C2 | semidirect |
| 5. #27163085 | C2 | semidirect |
| 6. #27163006 | C2 | semidirect |
| 7. C2×SD16×C397 | C2 | semidirect |
| 29. #15691787 | D4 | semidirect |
| 37. C8×C397 | D4 | semidirect |
| 54. C397 | #496 | semidirect |
| 57. C2×SD16 | D397 | semidirect |
| 92. C8 | C22⋊D397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263718 | 2 |
| C2×D3176 | 2 |
| C2×#20263716 | 2 |
| #27163092 | 2 |
| #27163085 | 2 |
| #27163006 | 2 |
| C2×SD16×C397 | 2 |
| #496 | 397 |