Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
230 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 51 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×#16812132 | C2 | semidirect |
| 2. C2×#16812052 | C2 | semidirect |
| 3. C2×D1712 | C2 | semidirect |
| 4. #20292864 | C2 | semidirect |
| 5. #20292427 | C2 | semidirect |
| 6. (C2×D107)⋊C16 | C2 | semidirect |
| 7. #358×C107 | C2 | semidirect |
| 35. D856 | D4 | semidirect |
| 43. Q16×C107 | D4 | semidirect |
| 90. C107 | #2186 | semidirect |
| 95. #358 | D107 | semidirect |
| 123. Q16 | D428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812132 | 2 |
| C2×#16812052 | 2 |
| C2×D1712 | 2 |
| #20292864 | 2 |
| #20292427 | 2 |
| (C2×D107)⋊C16 | 2 |
| #358×C107 | 2 |
| #2186 | 107 |