Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
512 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
| 5. #20292867 | C2 | direct (N × H) |
| 6. C2×#16812042 | C2 | semidirect |
| 7. C2×#16812034 | C2 | semidirect |
| 8. C2×#103×C107 | C2 | semidirect |
| 12. C2×#13133808 | C22 | semidirect |
| 25. #16812042 | C22 | semidirect |
| 26. #16812034 | C22 | semidirect |
| 30. #103×C107 | C22 | semidirect |
| 67. C22×D107 | Q16 | semidirect |
| 101. C2×D107 | C2×Q16 | semidirect |
| 110. C2×C107 | #467 | semidirect |
| 116. C107 | C2×#467 | semidirect |
| 124. C2×#103 | D107 | semidirect |
| 146. #103 | C2×D107 | semidirect |
| 227. C2 | #20292867 | 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×C8×D107 | 2 |
| C2×#16812089 | 2 |
| C2×#16812085 | 2 |
| #20292867 | 2 |
| C2×#16812042 | 2 |
| C2×#16812034 | 2 |
| C2×#103×C107 | 2 |
| C2×#467 | 107 |