Finite Group DatabasebetaFinite Group DatabasebetaOrder 26176.
148 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 45 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×Dic1636 | C2 | semidirect |
| 3. C2×#20266978 | C2 | semidirect |
| 5. #27189640 | C2 | semidirect |
| 7. #103×C409 | C2 | semidirect |
| 45. C2×D409 | Q16 | semidirect |
| 57. C409 | #451 | semidirect |
| 64. #103 | D409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D409 | 2 |
| C2×Dic1636 | 2 |
| C2×#20266978 | 2 |
| #27189697 | 2 |
| #27189640 | 2 |
| #27189629 | 2 |
| #103×C409 | 2 |
| #451 | 409 |