Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
260 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 79 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. #27164046 | C2 | semidirect |
| 3. #27164045 | C2 | semidirect |
| 6. #27163790 | C2 | semidirect |
| 7. #344×C199 | C2 | semidirect |
| 92. C199 | #1868 | semidirect |
| 100. #344 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164784 | 2 |
| #27164046 | 2 |
| #27164045 | 2 |
| #27163991 | 2 |
| #27163986 | 2 |
| #27163790 | 2 |
| #344×C199 | 2 |
| #1868 | 199 |