Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
184 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. C4⋊(C107⋊C16) | C2 | semidirect |
| 4. Dic107⋊C16 | C2 | semidirect |
| 5. C4⋊C16×C107 | C2 | semidirect |
| 40. C4×D107 | C16 | semidirect |
| 53. C4×C107 | C2×C16 | semidirect |
| 58. Dic107 | C2×C16 | semidirect |
| 62. D107 | C4⋊C16 | direct (N × H) |
| 64. C107 | C2×C4⋊C16 | semidirect |
| 69. C4⋊C16 | D107 | direct (N × H) |
| 120. C4 | C16×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×D107 | 2 |
| C4×C8×D107 | 2 |
| C4⋊(C107⋊C16) | 2 |
| Dic107⋊C16 | 2 |
| C4⋊C16×C107 | 2 |
| C2×C4⋊C16 | 107 |