Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
136 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 136 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. #27164419 | C2 | semidirect |
| 3. #27163845 | C2 | semidirect |
| 4. Dic199⋊C16 | C2 | semidirect |
| 7. #366×C199 | C2 | semidirect |
| 62. C199 | #2228 | semidirect |
| 67. #366 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164419 | 2 |
| #27164100 | 2 |
| #27163845 | 2 |
| Dic199⋊C16 | 2 |
| #27163820 | 2 |
| #27163818 | 2 |
| #366×C199 | 2 |
| #2228 | 199 |