Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
536 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 82 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. #20296025 | C2 | semidirect |
| 2. #20296019 | C2 | semidirect |
| 3. #20296012 | C2 | semidirect |
| 4. #20296005 | C2 | semidirect |
| 17. C2×#13182030 | C4 | semidirect |
| 21. C2×#13182029 | C4 | semidirect |
| 24. C2×Q8×D109 | C4 | semidirect |
| 26. C22×Q8×C109 | C4 | semidirect |
| 142. C109 | #1796 | semidirect |
| 160. C22×Q8 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296025 | 2 |
| #20296019 | 2 |
| #20296012 | 2 |
| #20296005 | 2 |
| C2×#16812747 | 2 |
| #1796 | 109 |