Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
608 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 197 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. C2×#15692983 | C2 | semidirect |
| 3. #20267902 | C2 | direct (N × H) |
| 4. C2×#15692941 | C2 | semidirect |
| 5. C2×#15692931 | C2 | semidirect |
| 6. C2×#106×C103 | C2 | semidirect |
| 9. C2×D824 | C4 | semidirect |
| 13. #15692983 | C22 | semidirect |
| 16. #15692941 | C22 | semidirect |
| 17. #15692931 | C22 | semidirect |
| 20. #106×C103 | C22 | semidirect |
| 24. C2×D412 | C2×C4 | semidirect |
| 29. D824 | C2×C4 | semidirect |
| 37. C2×C8×C103 | C2×C4 | semidirect |
| 56. D412 | C22×C4 | semidirect |
| 58. C8×C103 | C22×C4 | semidirect |
| 72. C2×C103 | #442 | semidirect |
| 77. C103 | C2×#442 | semidirect |
| 81. C2×#106 | D103 | semidirect |
| 95. #106 | C2×D103 | semidirect |
| 111. C2×C8 | C4×D103 | semidirect |
| 136. C8 | C2×C4×D103 | semidirect |
| 150. C2 | #20267902 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D824 | 2 |
| C2×#15692983 | 2 |
| #20267902 | 2 |
| C2×#15692941 | 2 |
| C2×#15692931 | 2 |
| C2×#106×C103 | 2 |
| C2×#442 | 103 |