Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16812101 | C2 | semidirect |
| 3. #20292982 | C2 | direct (N × H) |
| 4. C2×#16812034 | C2 | semidirect |
| 6. C2×C4×C8×C107 | C2 | semidirect |
| 10. #16812101 | C22 | semidirect |
| 16. #16812034 | C22 | semidirect |
| 20. C4×C8×C107 | C22 | semidirect |
| 69. C2×C107 | #488 | semidirect |
| 74. C107 | C2×#488 | semidirect |
| 80. C2×C4×C8 | D107 | semidirect |
| 94. C4×C8 | C2×D107 | semidirect |
| 144. C2 | #20292982 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812101 | 2 |
| C2×#16812097 | 2 |
| #20292982 | 2 |
| C2×#16812034 | 2 |
| C2×#16812031 | 2 |
| C2×C4×C8×C107 | 2 |
| C2×#488 | 107 |