Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
224 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 74 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. D109⋊M32 | C2 | semidirect |
| 2. C2×D109⋊C16 | C2 | semidirect |
| 3. #20295925 | C2 | semidirect |
| 4. #20295924 | C2 | semidirect |
| 7. #16812773 | C22 | semidirect |
| 11. C2×#13182032 | C22 | semidirect |
| 101. D109 | #350 | semidirect |
| 103. C109 | C2×#350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D109⋊M32 | 2 |
| C2×D109⋊C16 | 2 |
| #20295925 | 2 |
| #20295924 | 2 |
| #131×D109 | 2 |
| C2×#350 | 109 |