Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
452 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 137 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. #20295826 | C2 | semidirect |
| 2. C2×#16812721 | C2 | semidirect |
| 3. C2×#16812705 | C2 | semidirect |
| 4. #20295302 | C2 | semidirect |
| 5. #20295297 | C2 | semidirect |
| 6. #20295290 | C2 | semidirect |
| 7. #20295008 | C2 | semidirect |
| 8. C2×#108×C109 | C2 | semidirect |
| 20. C2×Dic436 | C22 | semidirect |
| 21. C2×#13182018 | C22 | semidirect |
| 22. C2×D872 | C22 | semidirect |
| 30. #16812617 | C22 | semidirect |
| 31. #16812615 | C22 | semidirect |
| 34. #108×C109 | C22 | semidirect |
| 35. #108×C109 | C22 | semidirect |
| 133. C109 | #3067 | semidirect |
| 140. C2×#108 | D109 | semidirect |
| 165. #108 | C2×D109 | semidirect |
| 166. #108 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295826 | 2 |
| C2×#16812721 | 2 |
| C2×#16812705 | 2 |
| #20295302 | 2 |
| #20295297 | 2 |
| #20295290 | 2 |
| #20295008 | 2 |
| C2×#108×C109 | 2 |
| #3067 | 109 |