Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
164 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 71 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×#20263265 | C2 | semidirect |
| 2. C22×#15691333 | C2 | semidirect |
| 4. #27160897 | C2 | semidirect |
| 5. #27160858 | C2 | semidirect |
| 6. #27160854 | C2 | semidirect |
| 7. C22⋊C16×C197 | C2 | semidirect |
| 32. #15691333 | D4 | semidirect |
| 59. C22×C197 | M32 | semidirect |
| 75. C197 | #2168 | semidirect |
| 82. C22⋊C16 | D197 | semidirect |
| 138. C22 | #20263265 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263265 | 2 |
| C22×#15691333 | 2 |
| C8×C22⋊D197 | 2 |
| #27160897 | 2 |
| #27160858 | 2 |
| #27160854 | 2 |
| C22⋊C16×C197 | 2 |
| #2168 | 197 |