Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 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 |
|---|---|---|
| 1. C22×#13133808 | C2 | semidirect |
| 4. C2×#16812107 | C2 | semidirect |
| 6. #20293020 | C2 | direct (N × H) |
| 7. C2×#16812019 | C2 | semidirect |
| 8. C22×Q16×C107 | C2 | semidirect |
| 12. C2×#13133808 | C22 | semidirect |
| 19. #16812107 | C22 | semidirect |
| 25. #16812019 | C22 | semidirect |
| 29. C2×Q16×C107 | C22 | semidirect |
| 108. C2×C107 | #497 | semidirect |
| 113. C107 | C2×#497 | semidirect |
| 115. C22×Q16 | D107 | semidirect |
| 129. C2×Q16 | C2×D107 | semidirect |
| 222. C2 | #20293020 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133808 | 2 |
| C22×#13133807 | 2 |
| C22×#13133805 | 2 |
| C2×#16812107 | 2 |
| C2×#16812098 | 2 |
| #20293020 | 2 |
| C2×#16812019 | 2 |
| C22×Q16×C107 | 2 |
| C2×#497 | 107 |