Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
230 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 81 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. #27161106 | C2 | semidirect |
| 4. C2×C8×Dic197 | C2 | semidirect |
| 5. #27160844 | C2 | semidirect |
| 6. #27160838 | C2 | semidirect |
| 19. #103×C197 | C4 | semidirect |
| 20. #102×C197 | C4 | semidirect |
| 90. C197 | #1937 | semidirect |
| 108. #103 | Dic197 | semidirect |
| 109. #102 | Dic197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161106 | 2 |
| C2×#20263253 | 2 |
| #27161046 | 2 |
| C2×C8×Dic197 | 2 |
| #27160844 | 2 |
| #27160838 | 2 |
| #416×C197 | 2 |
| #1937 | 197 |