Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
120 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 47 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. #27164420 | C2 | semidirect |
| 3. #27163841 | C2 | semidirect |
| 5. #364×C199 | C2 | semidirect |
| 50. C199 | #2231 | semidirect |
| 55. #364 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164420 | 2 |
| #27164136 | 2 |
| #27163841 | 2 |
| #27163829 | 2 |
| #364×C199 | 2 |
| #2231 | 199 |