Finite Group DatabasebetaFinite Group DatabasebetaOrder 25408.
158 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 55 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. C2×C8×D397 | C2 | semidirect |
| 3. #27163054 | C2 | semidirect |
| 4. #27163021 | C2 | semidirect |
| 5. #27163019 | C2 | semidirect |
| 6. #27163017 | C2 | semidirect |
| 7. #102×C397 | C2 | semidirect |
| 9. #20263730 | C4 | semidirect |
| 57. C397 | #416 | semidirect |
| 65. #102 | D397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263730 | 2 |
| C2×C8×D397 | 2 |
| #27163054 | 2 |
| #27163021 | 2 |
| #27163019 | 2 |
| #27163017 | 2 |
| #102×C397 | 2 |
| #416 | 397 |