Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#16812746 | C2 | semidirect |
| 2. #20295824 | C2 | semidirect |
| 3. #20295597 | C2 | semidirect |
| 4. #20295207 | C2 | semidirect |
| 5. #20295197 | C2 | semidirect |
| 6. #20295043 | C2 | semidirect |
| 7. #20295042 | C2 | semidirect |
| 8. C2×#16812617 | C2 | semidirect |
| 9. #575×C109 | C2 | semidirect |
| 21. #16812730 | C22 | semidirect |
| 23. #16812725 | C22 | semidirect |
| 27. #16812697 | C22 | semidirect |
| 28. #16812686 | C22 | semidirect |
| 32. #16812626 | C22 | semidirect |
| 33. #16812625 | C22 | semidirect |
| 34. #16812617 | C22 | semidirect |
| 38. #137×C109 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C109 | C22 | semidirect |
| 186. C109 | #3020 | semidirect |
| 189. #575 | D109 | semidirect |
| 212. #137 | C2×D109 | semidirect |
| 216. AGL(1,ℤ/8) | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812746 | 2 |
| #20295824 | 2 |
| #20295597 | 2 |
| #20295207 | 2 |
| #20295197 | 2 |
| #20295043 | 2 |
| #20295042 | 2 |
| C2×#16812617 | 2 |
| #575×C109 | 2 |
| #3020 | 109 |