Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
264 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 264 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. #27164015 | C2 | semidirect |
| 3. #27163991 | C2 | semidirect |
| 4. #27163775 | C2 | semidirect |
| 5. #424×C199 | C2 | semidirect |
| 74. C199 | #2053 | semidirect |
| 77. #424 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164818 | 2 |
| #27164015 | 2 |
| #27163991 | 2 |
| #27163775 | 2 |
| #424×C199 | 2 |
| #2053 | 199 |