Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
370 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 139 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. #27161808 | C2 | semidirect |
| 3. #27161430 | C2 | semidirect |
| 4. #27161365 | C2 | semidirect |
| 7. C8×Q8×C197 | C2 | semidirect |
| 53. Q8×C197 | SD16 | semidirect |
| 74. C197 | #3359 | semidirect |
| 81. C8×Q8 | D197 | semidirect |
| 122. Q8 | #15691347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161808 | 2 |
| Q8×D788 | 2 |
| #27161430 | 2 |
| #27161365 | 2 |
| #27161285 | 2 |
| C4×#15691347 | 2 |
| C8×Q8×C197 | 2 |
| #3359 | 197 |