Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
216 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 69 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. #20295074 | C2 | semidirect |
| 5. M16×Dic109 | C2 | semidirect |
| 6. #20294785 | C2 | semidirect |
| 7. #344×C109 | C2 | semidirect |
| 16. #16812617 | C4 | semidirect |
| 17. #16812615 | C4 | semidirect |
| 96. C109 | #1932 | semidirect |
| 102. #344 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295074 | 2 |
| #20295044 | 2 |
| C2×#16812625 | 2 |
| #20295008 | 2 |
| M16×Dic109 | 2 |
| #20294785 | 2 |
| #344×C109 | 2 |
| #1932 | 109 |