Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
552 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 157 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×#20263357 | C2 | semidirect |
| 3. #27161471 | C2 | semidirect |
| 4. #27161458 | C2 | semidirect |
| 5. #27161453 | C2 | semidirect |
| 6. C4×#15691342 | C2 | semidirect |
| 7. C2×C4⋊Q8×C197 | C2 | semidirect |
| 34. #15691342 | D4 | semidirect |
| 76. C4×C197 | #137 | semidirect |
| 83. C197 | #3152 | semidirect |
| 87. C2×C4⋊Q8 | D197 | semidirect |
| 161. C4 | #20263357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263357 | 2 |
| #27161629 | 2 |
| #27161471 | 2 |
| #27161458 | 2 |
| #27161453 | 2 |
| C4×#15691342 | 2 |
| C2×C4⋊Q8×C197 | 2 |
| #3152 | 197 |