Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 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. C22×#13182017 | C2 | semidirect |
| 2. #20295597 | C2 | semidirect |
| 3. #20295501 | C2 | semidirect |
| 4. #20295239 | C2 | semidirect |
| 5. #20295229 | C2 | semidirect |
| 6. #20295054 | C2 | semidirect |
| 7. #20295036 | C2 | semidirect |
| 8. #20295022 | C2 | semidirect |
| 14. #16812697 | C22 | semidirect |
| 15. #16812686 | C22 | semidirect |
| 23. #16812628 | C22 | semidirect |
| 24. #16812624 | C22 | semidirect |
| 25. #16812623 | C22 | semidirect |
| 26. #16812620 | C22 | semidirect |
| 117. C109 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182017 | 2 |
| #20295597 | 2 |
| #20295501 | 2 |
| #20295239 | 2 |
| #20295229 | 2 |
| #20295054 | 2 |
| #20295036 | 2 |
| #20295022 | 2 |
| C2×AGL(1,ℤ/8)×C109 | 2 |
| #3042 | 109 |