Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
452 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 177 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. #20292706 | C2 | semidirect |
| 3. #20292704 | C2 | semidirect |
| 4. #20292680 | C2 | semidirect |
| 5. #20292589 | C2 | semidirect |
| 6. #431×C107 | C2 | semidirect |
| 9. C2×#13133801 | C22 | semidirect |
| 16. C4⋊(C107⋊C8) | C22 | semidirect |
| 18. (C2×D107)⋊C8 | C22 | semidirect |
| 19. C4×C107⋊C8 | C22 | semidirect |
| 21. C4⋊C8×C107 | C22 | semidirect |
| 23. C4×C8×C107 | C22 | semidirect |
| 53. C2×C4×C107 | M16 | semidirect |
| 89. C107 | #2975 | semidirect |
| 94. #431 | D107 | semidirect |
| 107. C4⋊C8 | C2×D107 | semidirect |
| 112. C4×C8 | C2×D107 | semidirect |
| 148. C2×C4 | #13133801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D428 | 2 |
| #20292706 | 2 |
| #20292704 | 2 |
| #20292680 | 2 |
| #20292589 | 2 |
| #431×C107 | 2 |
| #2975 | 107 |