Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
284 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 73 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. #27160942 | C2 | semidirect |
| 3. #27160817 | C2 | semidirect |
| 4. #27160814 | C2 | semidirect |
| 5. C2×C22⋊C8×C197 | C2 | semidirect |
| 6. C2×#15691358 | C4 | semidirect |
| 8. #20263305 | C4 | semidirect |
| 10. #20263300 | C4 | semidirect |
| 15. #20263285 | C4 | semidirect |
| 111. C197 | #1516 | semidirect |
| 114. C2×C22⋊C8 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161590 | 2 |
| #27160942 | 2 |
| #27160817 | 2 |
| #27160814 | 2 |
| C2×C22⋊C8×C197 | 2 |
| #1516 | 197 |