Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
300 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. #27161037 | C2 | semidirect |
| 4. C2×C4×#13096802 | C2 | semidirect |
| 5. #27160843 | C2 | semidirect |
| 6. #27160839 | C2 | semidirect |
| 9. #20263333 | C4 | semidirect |
| 16. #20263250 | C4 | semidirect |
| 17. #20263247 | C4 | semidirect |
| 24. #104×C197 | C4 | semidirect |
| 98. C197 | #1764 | semidirect |
| 118. #104 | Dic197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263333 | 2 |
| #27161075 | 2 |
| #27161037 | 2 |
| C2×C4×#13096802 | 2 |
| #27160843 | 2 |
| #27160839 | 2 |
| C2×#104×C197 | 2 |
| #1764 | 197 |