Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
1240 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 1240 conjugacy classes of subgroups — too many to draw. Only its 501 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. #20268527 | C2 | direct (N × H) |
| 2. C2×#15693008 | C2 | semidirect |
| 3. C2×#15693002 | C2 | semidirect |
| 4. C2×C4×Dic206 | C2 | semidirect |
| 5. C2×D4×Dic103 | C2 | semidirect |
| 9. #15693008 | C22 | semidirect |
| 10. #15693002 | C22 | semidirect |
| 11. C4×Dic206 | C22 | semidirect |
| 12. D4×Dic103 | C22 | semidirect |
| 68. C2×C103 | #559 | semidirect |
| 72. C103 | C2×#559 | semidirect |
| 140. C2 | #20268527 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268527 | 2 |
| C2×#15693008 | 2 |
| C2×#15693002 | 2 |
| C2×C4×Dic206 | 2 |
| C2×D4×Dic103 | 2 |
| C2×#127×C103 | 2 |
| C2×#559 | 103 |