Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
164 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 71 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×C16×D107 | C2 | semidirect |
| 3. Dic107⋊C16 | C2 | semidirect |
| 4. C22⋊(C107⋊C16) | C2 | semidirect |
| 5. (C2×D107)⋊C16 | C2 | semidirect |
| 6. #20292402 | C2 | semidirect |
| 7. C2×M32×C107 | C2 | semidirect |
| 39. C16×C107 | D4 | semidirect |
| 63. C2×D107 | M32 | semidirect |
| 76. C107 | #2168 | semidirect |
| 77. C2×M32 | D107 | semidirect |
| 115. C16 | C22⋊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 |
| C8×C22⋊D107 | 2 |
| Dic107⋊C16 | 2 |
| C22⋊(C107⋊C16) | 2 |
| (C2×D107)⋊C16 | 2 |
| #20292402 | 2 |
| C2×M32×C107 | 2 |
| #2168 | 107 |