Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
232 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 93 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×#16812049 | C2 | semidirect |
| 2. C2×#16812041 | C2 | semidirect |
| 3. #20292437 | C2 | direct (N × H) |
| 7. #16812049 | C22 | semidirect |
| 10. #16812041 | C22 | semidirect |
| 14. #135×C107 | C4 | semidirect |
| 16. C2×Q16×C107 | C4 | semidirect |
| 18. C2×D8×C107 | C4 | semidirect |
| 34. Q16×C107 | C2×C4 | semidirect |
| 38. D8×C107 | C2×C4 | semidirect |
| 83. C2×C107 | #360 | semidirect |
| 86. C107 | C2×#360 | semidirect |
| 94. #135 | Dic107 | semidirect |
| 96. C2×Q16 | Dic107 | semidirect |
| 98. C2×D8 | Dic107 | semidirect |
| 117. Q16 | C2×Dic107 | semidirect |
| 121. D8 | C2×Dic107 | semidirect |
| 169. C2 | #20292437 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812049 | 2 |
| C2×#16812041 | 2 |
| #20292437 | 2 |
| C2×#135×C107 | 2 |
| C2×#360 | 107 |