Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
154 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 53 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. #27164141 | C2 | semidirect |
| 3. #27163840 | C2 | semidirect |
| 4. #27163831 | C2 | semidirect |
| 5. #27163827 | C2 | semidirect |
| 6. #27163796 | C2 | semidirect |
| 7. #442×C199 | C2 | semidirect |
| 10. #20263899 | C4 | semidirect |
| 11. #20263896 | C4 | semidirect |
| 22. Dic796 | C2×C4 | semidirect |
| 24. D1592 | C2×C4 | semidirect |
| 29. C199⋊C16 | C2×C4 | semidirect |
| 68. C199 | AGL(1,ℤ/16) | semidirect |
| 72. #442 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164454 | 2 |
| #27164141 | 2 |
| #27163840 | 2 |
| #27163831 | 2 |
| #27163827 | 2 |
| #27163796 | 2 |
| #442×C199 | 2 |
| AGL(1,ℤ/16) | 199 |