Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
492 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 3. #20292882 | C2 | direct (N × H) |
| 4. C2×#16812041 | C2 | semidirect |
| 5. C2×#16812033 | C2 | semidirect |
| 6. C22×Q16×C107 | C2 | semidirect |
| 16. #16812041 | C22 | semidirect |
| 17. #16812033 | C22 | semidirect |
| 20. C2×Q16×C107 | C22 | semidirect |
| 79. C2×C107 | #470 | semidirect |
| 84. C107 | C2×#470 | semidirect |
| 85. C22×Q16 | D107 | semidirect |
| 94. C2×Q16 | C2×D107 | semidirect |
| 164. C2 | #20292882 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133801 | 2 |
| C2×#16812085 | 2 |
| #20292882 | 2 |
| C2×#16812041 | 2 |
| C2×#16812033 | 2 |
| C22×Q16×C107 | 2 |
| C2×#470 | 107 |