Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16812721 | C2 | semidirect |
| 2. #20295537 | C2 | semidirect |
| 3. #20295284 | C2 | semidirect |
| 4. #20295279 | C2 | semidirect |
| 5. #20295272 | C2 | semidirect |
| 6. #20295064 | C2 | semidirect |
| 7. #20295023 | C2 | semidirect |
| 8. C22×M16×C109 | C2 | semidirect |
| 11. C2×Dic436 | C22 | semidirect |
| 12. C2×#13182018 | C22 | semidirect |
| 13. C2×D872 | C22 | semidirect |
| 20. #16812633 | C22 | semidirect |
| 21. #16812631 | C22 | semidirect |
| 22. #16812624 | C22 | semidirect |
| 23. #16812621 | C22 | semidirect |
| 56. C2×C8×C109 | D4 | semidirect |
| 106. C109 | #3054 | semidirect |
| 108. C22×M16 | D109 | semidirect |
| 156. C2×C8 | C22⋊D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812721 | 2 |
| #20295537 | 2 |
| #20295284 | 2 |
| #20295279 | 2 |
| #20295272 | 2 |
| #20295064 | 2 |
| #20295023 | 2 |
| C22×M16×C109 | 2 |
| #3054 | 109 |