Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
334 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #27164028 | C2 | semidirect |
| 4. #27163924 | C2 | semidirect |
| 5. #27163786 | C2 | semidirect |
| 6. #27163778 | C2 | semidirect |
| 10. #20263985 | C4 | semidirect |
| 33. C2×Dic398 | C2×C4 | semidirect |
| 40. #15691870 | C2×C4 | semidirect |
| 124. C199 | #1882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263985 | 2 |
| #27164501 | 2 |
| #27164028 | 2 |
| #27163924 | 2 |
| #27163786 | 2 |
| #27163778 | 2 |
| C2×#104×C199 | 2 |
| #1882 | 199 |