Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
564 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 564 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. C2×#16812722 | C2 | semidirect |
| 2. C2×#16812720 | C2 | semidirect |
| 3. #20295577 | C2 | semidirect |
| 4. #20295575 | C2 | semidirect |
| 5. #20295419 | C2 | semidirect |
| 6. #20295418 | C2 | semidirect |
| 7. #20295416 | C2 | semidirect |
| 8. #20295415 | C2 | semidirect |
| 9. #20295412 | C2 | semidirect |
| 10. #97×D109 | C2 | semidirect |
| 11. #497×C109 | C2 | semidirect |
| 65. C8×D109 | D4 | semidirect |
| 134. C109 | #3150 | semidirect |
| 141. #497 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812722 | 2 |
| C2×#16812720 | 2 |
| #20295577 | 2 |
| #20295575 | 2 |
| #20295419 | 2 |
| #20295418 | 2 |
| #20295416 | 2 |
| #20295415 | 2 |
| #20295412 | 2 |
| #97×D109 | 2 |
| #497×C109 | 2 |
| #3150 | 109 |