Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
500 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 229 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. C2×#20263333 | C2 | semidirect |
| 2. #27161157 | C2 | semidirect |
| 3. D4×#13096802 | C2 | semidirect |
| 4. #27161103 | C2 | semidirect |
| 5. #27161046 | C2 | semidirect |
| 6. C2×C4×#13096802 | C2 | semidirect |
| 29. C2×#13096802 | D4 | semidirect |
| 76. C4×C197 | #131 | semidirect |
| 83. C197 | #2931 | semidirect |
| 160. C4 | #20263333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263333 | 2 |
| #27161157 | 2 |
| D4×#13096802 | 2 |
| #27161103 | 2 |
| #27161046 | 2 |
| C2×C4×#13096802 | 2 |
| #532×C197 | 2 |
| #2931 | 197 |