Finite Group DatabasebetaFinite Group DatabasebetaOrder 26176.
114 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 39 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. C4⋊C4×D409 | C2 | semidirect |
| 3. #27189650 | C2 | semidirect |
| 4. #27189639 | C2 | semidirect |
| 5. #27189637 | C2 | semidirect |
| 6. #27189629 | C2 | semidirect |
| 7. #107×C409 | C2 | semidirect |
| 52. C409 | #480 | semidirect |
| 57. #107 | D409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27189692 | 2 |
| C4⋊C4×D409 | 2 |
| #27189650 | 2 |
| #27189639 | 2 |
| #27189637 | 2 |
| #27189629 | 2 |
| #107×C409 | 2 |
| #480 | 409 |