Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
220 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 47 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. #20295827 | C2 | semidirect |
| 2. #20295464 | C2 | semidirect |
| 3. C2×#16812640 | C2 | semidirect |
| 4. #20295297 | C2 | semidirect |
| 5. #20294832 | C2 | semidirect |
| 6. #20294811 | C2 | semidirect |
| 7. #361×C109 | C2 | semidirect |
| 14. C2×D872 | C22 | semidirect |
| 20. C2×#13182004 | C22 | semidirect |
| 23. M32×C109 | C22 | semidirect |
| 24. #108×C109 | C22 | semidirect |
| 94. C109 | #2192 | semidirect |
| 99. #361 | D109 | semidirect |
| 115. M32 | C2×D109 | semidirect |
| 117. #108 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295827 | 2 |
| #20295464 | 2 |
| C2×#16812640 | 2 |
| #20295297 | 2 |
| #20294832 | 2 |
| #20294811 | 2 |
| #361×C109 | 2 |
| #2192 | 109 |