Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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. C4×#15691886 | C2 | semidirect |
| 3. #27164036 | C2 | semidirect |
| 4. C2×#20263883 | C2 | semidirect |
| 5. #27163991 | C2 | semidirect |
| 6. #27163790 | C2 | semidirect |
| 7. #339×C199 | C2 | semidirect |
| 11. #20263988 | C4 | semidirect |
| 13. #20263983 | C4 | semidirect |
| 37. C2×Dic398 | C2×C4 | semidirect |
| 39. C2×D796 | C2×C4 | semidirect |
| 62. M16×C199 | C2×C4 | semidirect |
| 129. C199 | #1906 | semidirect |
| 137. #339 | D199 | semidirect |
| 185. M16 | C4×D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164818 | 2 |
| C4×#15691886 | 2 |
| #27164036 | 2 |
| C2×#20263883 | 2 |
| #27163991 | 2 |
| #27163790 | 2 |
| #339×C199 | 2 |
| #1906 | 199 |