Finite Group DatabasebetaFinite Group DatabasebetaOrder 26176.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #27189712 | C2 | semidirect |
| 2. #27189708 | C2 | semidirect |
| 3. #27189706 | C2 | semidirect |
| 4. #27189702 | C2 | semidirect |
| 5. #27189693 | C2 | semidirect |
| 7. C4×D1636 | C2 | semidirect |
| 8. C4×D1636 | C2 | semidirect |
| 9. #27189674 | C2 | semidirect |
| 10. C42×D409 | C2 | semidirect |
| 11. C4×Q8×C409 | C2 | semidirect |
| 74. C409 | #529 | semidirect |
| 82. C4×Q8 | D409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27189712 | 2 |
| #27189708 | 2 |
| #27189706 | 2 |
| #27189702 | 2 |
| #27189693 | 2 |
| #27189692 | 2 |
| C4×D1636 | 2 |
| #27189674 | 2 |
| C42×D409 | 2 |
| C4×Q8×C409 | 2 |
| #529 | 409 |