Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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. #20295697 | C2 | semidirect |
| 3. #20295402 | C2 | semidirect |
| 4. #20295260 | C2 | semidirect |
| 5. #20295226 | C2 | semidirect |
| 6. #20295223 | C2 | semidirect |
| 7. #20295171 | C2 | semidirect |
| 8. #20295169 | C2 | semidirect |
| 9. C4×#13182019 | C2 | semidirect |
| 10. D4×#11724784 | C2 | semidirect |
| 11. #550×C109 | C2 | semidirect |
| 51. #13182019 | D4 | semidirect |
| 131. C4×C109 | #135 | semidirect |
| 143. C109 | #3287 | semidirect |
| 146. #550 | D109 | semidirect |
| 276. C4 | #16812719 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812719 | 2 |
| #20295697 | 2 |
| #20295402 | 2 |
| #20295260 | 2 |
| #20295226 | 2 |
| #20295223 | 2 |
| #20295171 | 2 |
| #20295169 | 2 |
| C4×#13182019 | 2 |
| D4×#11724784 | 2 |
| #550×C109 | 2 |
| #3287 | 109 |