Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
544 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 173 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×#16812109 | C2 | semidirect |
| 4. #20292833 | C2 | direct (N × H) |
| 5. C2×#16812034 | C2 | semidirect |
| 6. C2×C4⋊C8×C107 | C2 | semidirect |
| 13. #16812109 | C22 | semidirect |
| 20. #16812034 | C22 | semidirect |
| 23. C4⋊C8×C107 | C22 | semidirect |
| 56. C2×C4×C107 | SD16 | semidirect |
| 85. C4×C107 | C2×SD16 | semidirect |
| 90. C2×C107 | #461 | semidirect |
| 96. C107 | C2×#461 | semidirect |
| 101. C2×C4⋊C8 | D107 | semidirect |
| 118. C4⋊C8 | C2×D107 | semidirect |
| 163. C2×C4 | #13133807 | semidirect |
| 183. C4 | C2×#13133807 | semidirect |
| 187. C2 | #20292833 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133807 | 2 |
| C2×#16812109 | 2 |
| C2×C4×D428 | 2 |
| #20292833 | 2 |
| C2×#16812034 | 2 |
| C2×C4⋊C8×C107 | 2 |
| C2×#461 | 107 |