Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×D412 | C2 | semidirect |
| 3. #20268142 | C2 | semidirect |
| 4. #20268123 | C2 | semidirect |
| 5. #20268076 | C2 | semidirect |
| 6. #20268019 | C2 | semidirect |
| 7. #20267996 | C2 | semidirect |
| 8. #20267928 | C2 | semidirect |
| 9. C8×D412 | C2 | semidirect |
| 10. #103×D103 | C2 | semidirect |
| 11. C4×SD16×C103 | C2 | semidirect |
| 80. Q8×C103 | #41 | semidirect |
| 94. D412 | SD16 | semidirect |
| 129. C103 | #3298 | semidirect |
| 138. C4×SD16 | D103 | semidirect |
| 213. Q8 | #13110105 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D412 | 2 |
| #20268446 | 2 |
| #20268142 | 2 |
| #20268123 | 2 |
| #20268076 | 2 |
| #20268019 | 2 |
| #20267996 | 2 |
| #20267928 | 2 |
| C8×D412 | 2 |
| #103×D103 | 2 |
| C4×SD16×C103 | 2 |
| #3298 | 103 |