Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
752 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 181 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×#16812107 | C2 | semidirect |
| 3. C2×#16812098 | C2 | semidirect |
| 4. C2×#16812097 | C2 | semidirect |
| 5. C2×#16812096 | C2 | semidirect |
| 6. #20292527 | C2 | semidirect |
| 7. C42×Dic107 | C2 | semidirect |
| 8. C2×#124×C107 | C2 | semidirect |
| 47. C4×Dic107 | D4 | semidirect |
| 59. C42×C107 | D4 | semidirect |
| 106. Dic107 | #124 | semidirect |
| 114. C107 | #2858 | semidirect |
| 120. C2×#124 | D107 | semidirect |
| 173. C42 | C22⋊D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812107 | 2 |
| C2×#16812105 | 2 |
| C2×#16812098 | 2 |
| C2×#16812097 | 2 |
| C2×#16812096 | 2 |
| #20292527 | 2 |
| C42×Dic107 | 2 |
| C2×#124×C107 | 2 |
| #2858 | 107 |