Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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×Dic796 | C2 | semidirect |
| 4. #27163846 | C2 | semidirect |
| 5. #27163823 | C2 | semidirect |
| 7. C4×C16×C199 | C2 | semidirect |
| 12. #20263900 | C4 | direct (N × H) |
| 24. Dic796 | C2×C4 | semidirect |
| 36. C16×C199 | C2×C4 | semidirect |
| 57. C4×C199 | SD32 | semidirect |
| 67. C199 | C4×SD32 | semidirect |
| 75. C4×C16 | D199 | semidirect |
| 104. C16 | C4×D199 | semidirect |
| 128. C4 | #20263900 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263900 | 2 |
| C4×Dic796 | 2 |
| C4×D1592 | 2 |
| #27163846 | 2 |
| #27163823 | 2 |
| #27163820 | 2 |
| C4×C16×C199 | 2 |
| C4×SD32 | 199 |