Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
144 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 144 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 |
|---|---|---|
| 1. #27164434 | C2 | semidirect |
| 3. #27163838 | C2 | semidirect |
| 4. #27163803 | C2 | semidirect |
| 5. #27163802 | C2 | semidirect |
| 6. #27163793 | C2 | semidirect |
| 7. #504×C199 | C2 | semidirect |
| 71. C199 | #2171 | semidirect |
| 74. #504 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164434 | 2 |
| #27164133 | 2 |
| #27163838 | 2 |
| #27163803 | 2 |
| #27163802 | 2 |
| #27163793 | 2 |
| #504×C199 | 2 |
| #2171 | 199 |