Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16812706 | C2 | semidirect |
| 3. #20295604 | C2 | semidirect |
| 4. #20295282 | C2 | semidirect |
| 5. #20295277 | C2 | semidirect |
| 6. #20295257 | C2 | semidirect |
| 7. #20295253 | C2 | semidirect |
| 8. C2×#16812630 | C2 | semidirect |
| 9. #20295027 | C2 | semidirect |
| 10. #20295025 | C2 | semidirect |
| 11. #537×C109 | C2 | semidirect |
| 58. C2×#11724784 | D4 | semidirect |
| 153. C109 | #3060 | semidirect |
| 157. #537 | 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×#16812706 | 2 |
| #20295604 | 2 |
| #20295282 | 2 |
| #20295277 | 2 |
| #20295257 | 2 |
| #20295253 | 2 |
| C2×#16812630 | 2 |
| #20295027 | 2 |
| #20295025 | 2 |
| #537×C109 | 2 |
| #3060 | 109 |