Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
544 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 2. C2×#16812697 | C2 | semidirect |
| 4. #20295229 | C2 | direct (N × H) |
| 5. C2×#16812628 | C2 | semidirect |
| 6. C2×#16812624 | C2 | semidirect |
| 7. C2×#16812623 | C2 | semidirect |
| 15. #16812697 | C22 | semidirect |
| 23. #16812628 | C22 | semidirect |
| 24. #16812624 | C22 | semidirect |
| 25. #16812623 | C22 | semidirect |
| 88. C2×Dic109 | SD16 | semidirect |
| 111. Dic109 | C2×SD16 | semidirect |
| 113. C2×C109 | #461 | semidirect |
| 118. C109 | C2×#461 | semidirect |
| 231. C2 | #20295229 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182017 | 2 |
| C2×#16812697 | 2 |
| C2×D4×Dic109 | 2 |
| #20295229 | 2 |
| C2×#16812628 | 2 |
| C2×#16812624 | 2 |
| C2×#16812623 | 2 |
| C22×SD16×C109 | 2 |
| C2×#461 | 109 |