Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
224 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 65 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. M32×D107 | C2 | semidirect |
| 3. #20292662 | C2 | semidirect |
| 4. #20292438 | C2 | semidirect |
| 5. #20292437 | C2 | semidirect |
| 6. #20292436 | C2 | semidirect |
| 7. #360×C107 | C2 | semidirect |
| 9. #16812132 | C4 | semidirect |
| 13. #16812128 | C4 | semidirect |
| 14. Q16×D107 | C4 | semidirect |
| 16. D8×D107 | C4 | semidirect |
| 19. #16812049 | C22 | semidirect |
| 23. #16812041 | C22 | semidirect |
| 25. M32×C107 | C22 | semidirect |
| 26. #106×C107 | C22 | semidirect |
| 111. C107 | #2145 | semidirect |
| 118. #360 | D107 | semidirect |
| 133. M32 | C2×D107 | semidirect |
| 137. #106 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×D107 | 2 |
| M32×D107 | 2 |
| #20292662 | 2 |
| #20292438 | 2 |
| #20292437 | 2 |
| #20292436 | 2 |
| #360×C107 | 2 |
| #2145 | 107 |