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. #27189710 | C2 | semidirect |
| 2. #27189708 | C2 | semidirect |
| 3. #27189704 | C2 | semidirect |
| 4. #27189699 | C2 | semidirect |
| 5. #27189697 | C2 | semidirect |
| 7. C4×Dic818 | C2 | semidirect |
| 8. C4×C22⋊D409 | C2 | semidirect |
| 9. #27189676 | C2 | semidirect |
| 10. C42×D409 | C2 | semidirect |
| 11. C4×D4×C409 | C2 | semidirect |
| 74. C409 | #529 | semidirect |
| 84. C4×D4 | D409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27189710 | 2 |
| #27189708 | 2 |
| #27189704 | 2 |
| #27189699 | 2 |
| #27189697 | 2 |
| #27189688 | 2 |
| C4×Dic818 | 2 |
| C4×C22⋊D409 | 2 |
| #27189676 | 2 |
| C42×D409 | 2 |
| C4×D4×C409 | 2 |
| #529 | 409 |