Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
412 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 78 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×D109⋊M16 | C2 | semidirect |
| 2. C2×#16812761 | C2 | semidirect |
| 3. #20295968 | C2 | semidirect |
| 4. #20295899 | C2 | semidirect |
| 17. #16812674 | C4 | semidirect |
| 18. #16812673 | C4 | semidirect |
| 21. #16812670 | C4 | semidirect |
| 24. #121×C109 | C4 | semidirect |
| 29. D109⋊C8 | D4 | semidirect |
| 142. C109 | #1895 | semidirect |
| 160. #121 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D109⋊M16 | 2 |
| C2×#16812761 | 2 |
| #20295968 | 2 |
| #20295899 | 2 |
| #121×D109 | 2 |
| #1895 | 109 |