Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
222 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 222 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. #27164045 | C2 | semidirect |
| 4. C2×#20263865 | C2 | semidirect |
| 5. #27163783 | C2 | semidirect |
| 6. #27163777 | C2 | semidirect |
| 19. #103×C199 | C4 | semidirect |
| 20. #102×C199 | C4 | semidirect |
| 90. C199 | #1938 | semidirect |
| 108. #103 | Dic199 | semidirect |
| 109. #102 | Dic199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164045 | 2 |
| C2×#20263882 | 2 |
| #27163985 | 2 |
| C2×#20263865 | 2 |
| #27163783 | 2 |
| #27163777 | 2 |
| #416×C199 | 2 |
| #1938 | 199 |