Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
336 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 336 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×#16812762 | C2 | semidirect |
| 3. C4×D109⋊C8 | C2 | semidirect |
| 4. #20295970 | C2 | semidirect |
| 14. #16812688 | C4 | semidirect |
| 15. #16812687 | C4 | semidirect |
| 16. #16812686 | C4 | semidirect |
| 20. #124×C109 | C4 | semidirect |
| 98. C109 | #1958 | semidirect |
| 111. #124 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812762 | 2 |
| C2×#16812761 | 2 |
| C4×D109⋊C8 | 2 |
| #20295970 | 2 |
| #124×D109 | 2 |
| #1958 | 109 |