Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
792 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 229 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. C22×C8×D103 | C2 | semidirect |
| 3. C2×#15692979 | C2 | semidirect |
| 4. #20267784 | C2 | direct (N × H) |
| 5. C2×#15692946 | C2 | semidirect |
| 6. C2×#15692944 | C2 | semidirect |
| 7. C2×#15692942 | C2 | semidirect |
| 8. C2×#102×C103 | C2 | semidirect |
| 11. C2×#13110104 | C4 | semidirect |
| 19. C2×C8×D103 | C22 | semidirect |
| 21. #15692979 | C22 | semidirect |
| 25. #15692946 | C22 | semidirect |
| 26. #15692944 | C22 | semidirect |
| 27. #15692942 | C22 | semidirect |
| 31. #102×C103 | C22 | semidirect |
| 35. #13110104 | C2×C4 | semidirect |
| 123. C2×C103 | #416 | semidirect |
| 129. C103 | C2×#416 | semidirect |
| 137. C2×#102 | D103 | semidirect |
| 160. #102 | C2×D103 | semidirect |
| 253. C2 | #20267784 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13110104 | 2 |
| C22×C8×D103 | 2 |
| C2×#15692979 | 2 |
| #20267784 | 2 |
| C2×#15692946 | 2 |
| C2×#15692944 | 2 |
| C2×#15692942 | 2 |
| C2×#102×C103 | 2 |
| C2×#416 | 103 |