Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 2. #27161483 | C2 | semidirect |
| 3. #27161457 | C2 | semidirect |
| 4. #27161428 | C2 | semidirect |
| 8. C4×Dic788 | C2 | semidirect |
| 9. C4×#15691348 | C2 | semidirect |
| 11. C4×Q16×C197 | C2 | semidirect |
| 83. C4×D197 | Q16 | semidirect |
| 114. C197 | #3170 | semidirect |
| 125. C4×Q16 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161633 | 2 |
| #27161483 | 2 |
| #27161457 | 2 |
| #27161428 | 2 |
| #27161321 | 2 |
| #27161319 | 2 |
| #27161317 | 2 |
| C4×Dic788 | 2 |
| C4×#15691348 | 2 |
| C4×C8×D197 | 2 |
| C4×Q16×C197 | 2 |
| #3170 | 197 |