Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
284 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 66 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. #20296036 | C2 | semidirect |
| 2. #20296025 | C2 | semidirect |
| 3. #20296024 | C2 | semidirect |
| 4. #20296007 | C2 | semidirect |
| 5. #20296006 | C2 | semidirect |
| 6. #20295989 | C2 | semidirect |
| 26. C2×#13182019 | C4 | semidirect |
| 27. C2×#13182018 | C4 | semidirect |
| 28. C2×#13182014 | C4 | semidirect |
| 30. C2×SD16×C109 | C4 | semidirect |
| 133. C109 | #1976 | semidirect |
| 149. C2×SD16 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296036 | 2 |
| #20296025 | 2 |
| #20296024 | 2 |
| #20296007 | 2 |
| #20296006 | 2 |
| #20295989 | 2 |
| C2×#16812720 | 2 |
| #1976 | 109 |