Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
1080 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 565 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. #27161710 | C2 | direct (N × H) |
| 2. C2×#20263325 | C2 | semidirect |
| 3. C2×#20263317 | C2 | semidirect |
| 8. #20263325 | C22 | semidirect |
| 9. #20263317 | C22 | semidirect |
| 34. C22×C4×C197 | Q8 | semidirect |
| 53. C2×C4×C197 | C2×Q8 | semidirect |
| 69. C2×C197 | #544 | semidirect |
| 73. C197 | C2×#544 | semidirect |
| 102. C22×C4 | Dic394 | semidirect |
| 127. C2×C4 | C2×Dic394 | semidirect |
| 143. C2 | #27161710 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161710 | 2 |
| C2×#20263325 | 2 |
| C2×#20263317 | 2 |
| C2×#20263305 | 2 |
| C2×#20263285 | 2 |
| C22×C4⋊C4×C197 | 2 |
| C2×#544 | 197 |