Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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×#16812719 | C2 | semidirect |
| 2. C2×#16812707 | C2 | semidirect |
| 3. #20295607 | C2 | semidirect |
| 4. #20295604 | C2 | semidirect |
| 5. #20295275 | C2 | semidirect |
| 6. #20295271 | C2 | semidirect |
| 7. #20295266 | C2 | semidirect |
| 8. #20295261 | C2 | semidirect |
| 9. C2×#16812632 | C2 | semidirect |
| 10. #20295028 | C2 | semidirect |
| 11. #417×C109 | C2 | semidirect |
| 63. C2×#11724784 | D4 | semidirect |
| 153. C109 | #3061 | semidirect |
| 164. #417 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812719 | 2 |
| C2×#16812707 | 2 |
| #20295607 | 2 |
| #20295604 | 2 |
| #20295275 | 2 |
| #20295271 | 2 |
| #20295266 | 2 |
| #20295261 | 2 |
| C2×#16812632 | 2 |
| #20295028 | 2 |
| #417×C109 | 2 |
| #3061 | 109 |