Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
374 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. C2×Q8×Dic107 | C2 | semidirect |
| 5. #20292389 | C2 | semidirect |
| 6. #20292381 | C2 | semidirect |
| 7. C2×#103×C107 | C2 | semidirect |
| 11. C2×#13133805 | C4 | semidirect |
| 73. Q8×C107 | C22⋊C4 | semidirect |
| 94. C2×Dic107 | SD16 | semidirect |
| 133. C107 | #1880 | semidirect |
| 136. C2×#103 | D107 | semidirect |
| 206. Q8 | (C2×D107)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133805 | 2 |
| C2×Q8×Dic107 | 2 |
| C2×#16812031 | 2 |
| #20292528 | 2 |
| #20292389 | 2 |
| #20292381 | 2 |
| C2×#103×C107 | 2 |
| #1880 | 107 |