Finite Group DatabasebetaFinite Group DatabasebetaOrder 26176.
124 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 51 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. C2×#20266972 | C2 | semidirect |
| 2. C2×C8×D409 | C2 | semidirect |
| 4. #27189646 | C2 | semidirect |
| 5. #27189629 | C2 | semidirect |
| 6. #27189627 | C2 | semidirect |
| 7. C22⋊C8×C409 | C2 | semidirect |
| 29. #15692543 | D4 | semidirect |
| 43. C2×D409 | M16 | semidirect |
| 55. C409 | #435 | semidirect |
| 62. C22⋊C8 | D409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20266972 | 2 |
| C2×C8×D409 | 2 |
| C4×C22⋊D409 | 2 |
| #27189646 | 2 |
| #27189629 | 2 |
| #27189627 | 2 |
| C22⋊C8×C409 | 2 |
| #435 | 409 |