Finite Group DatabasebetaFinite Group DatabasebetaOrder 25664.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×Q8×D401 | C2 | semidirect |
| 3. #27165736 | C2 | semidirect |
| 4. #27165723 | C2 | semidirect |
| 5. #27165722 | C2 | semidirect |
| 6. #27165719 | C2 | semidirect |
| 7. #27165717 | C2 | semidirect |
| 8. #27165716 | C2 | semidirect |
| 9. #27165713 | C2 | semidirect |
| 10. #27165695 | C2 | semidirect |
| 11. C22⋊Q8×C401 | C2 | semidirect |
| 83. C401 | #536 | semidirect |
| 94. C22⋊Q8 | D401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20264366 | 2 |
| C2×Q8×D401 | 2 |
| #27165736 | 2 |
| #27165723 | 2 |
| #27165722 | 2 |
| #27165719 | 2 |
| #27165717 | 2 |
| #27165716 | 2 |
| #27165713 | 2 |
| #27165695 | 2 |
| C22⋊Q8×C401 | 2 |
| #536 | 401 |