Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
180 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 73 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. #27164142 | C2 | semidirect |
| 4. #27163768 | C2 | semidirect |
| 5. #27163750 | C2 | semidirect |
| 6. C8×C199⋊C8 | C2 | semidirect |
| 24. #15691874 | C8 | semidirect |
| 42. Dic398 | C2×C8 | semidirect |
| 48. C199⋊C8 | C2×C8 | semidirect |
| 49. C199⋊C8 | SD16 | semidirect |
| 77. C199 | C8×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164142 | 2 |
| C4×#15691874 | 2 |
| D4×C199⋊C8 | 2 |
| #27163768 | 2 |
| #27163750 | 2 |
| C8×C199⋊C8 | 2 |
| D4⋊C8×C199 | 2 |
| C8×SD16 | 199 |