Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
178 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 57 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. #27164370 | C2 | semidirect |
| 2. #27164369 | C2 | semidirect |
| 3. #27164368 | C2 | semidirect |
| 6. C8×C199⋊C8 | C2 | semidirect |
| 67. C199 | #1711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164370 | 2 |
| #27164369 | 2 |
| #27164368 | 2 |
| #27164364 | 2 |
| C8×C199⋊C8 | 2 |
| #486×C199 | 2 |
| #1711 | 199 |