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×#16812043 | C2 | semidirect |
| 3. #20292431 | C2 | semidirect |
| 4. #20292428 | C2 | semidirect |
| 13. #135×C107 | C4 | semidirect |
| 30. Q16×C107 | C2×C4 | semidirect |
| 33. D8×C107 | C2×C4 | semidirect |
| 74. C107 | #2139 | semidirect |
| 82. #135 | Dic107 | semidirect |
| 101. Q16 | C2×Dic107 | semidirect |
| 104. D8 | C2×Dic107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812049 | 2 |
| C2×#16812043 | 2 |
| #20292431 | 2 |
| #20292428 | 2 |
| C2×#135×C107 | 2 |
| #2139 | 107 |