Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
696 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 189 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×#16812687 | C2 | semidirect |
| 2. C2×#16812678 | C2 | semidirect |
| 4. #20294932 | C2 | semidirect |
| 5. #20294928 | C2 | semidirect |
| 6. #20294917 | C2 | semidirect |
| 7. #20294905 | C2 | semidirect |
| 8. #20294892 | C2 | semidirect |
| 9. C22×C42×C109 | C2 | semidirect |
| 63. C42×C109 | D4 | semidirect |
| 103. C22×C109 | #124 | semidirect |
| 129. C109 | #2850 | semidirect |
| 133. C22×C42 | D109 | semidirect |
| 192. C42 | C22⋊D109 | semidirect |
| 237. C22 | #16812687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812687 | 2 |
| C2×#16812678 | 2 |
| C2×#16812673 | 2 |
| #20294932 | 2 |
| #20294928 | 2 |
| #20294917 | 2 |
| #20294905 | 2 |
| #20294892 | 2 |
| C22×C42×C109 | 2 |
| #2850 | 109 |