Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 444 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×#16812085 | C2 | semidirect |
| 3. C2×#16812033 | C2 | semidirect |
| 4. C2×#16812030 | C2 | semidirect |
| 5. C2×(C2×D107)⋊C8 | C2 | semidirect |
| 6. #20292390 | C2 | semidirect |
| 7. C22×SD16×C107 | C2 | semidirect |
| 48. C4⋊Dic107 | D4 | semidirect |
| 58. C2×Q8×C107 | D4 | semidirect |
| 70. C2×C8×C107 | D4 | semidirect |
| 85. C22×D107 | SD16 | semidirect |
| 158. C107 | #2000 | semidirect |
| 159. C22×SD16 | D107 | semidirect |
| 194. C2×Q8 | C22⋊D107 | semidirect |
| 221. C2×C8 | C22⋊D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812085 | 2 |
| C2×#16812080 | 2 |
| C2×#16812033 | 2 |
| C2×#16812030 | 2 |
| C2×(C2×D107)⋊C8 | 2 |
| #20292390 | 2 |
| C22×SD16×C107 | 2 |
| #2000 | 107 |