Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 3. #20268142 | C2 | semidirect |
| 4. #20268128 | C2 | semidirect |
| 5. #20268086 | C2 | semidirect |
| 6. #20268031 | C2 | semidirect |
| 7. #20268001 | C2 | semidirect |
| 8. #20267945 | C2 | semidirect |
| 10. #103×D103 | C2 | semidirect |
| 11. C4×Q16×C103 | C2 | semidirect |
| 91. D412 | Q16 | semidirect |
| 123. C103 | #3299 | semidirect |
| 132. C4×Q16 | D103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268501 | 2 |
| Q8×D412 | 2 |
| #20268142 | 2 |
| #20268128 | 2 |
| #20268086 | 2 |
| #20268031 | 2 |
| #20268001 | 2 |
| #20267945 | 2 |
| C8×D412 | 2 |
| #103×D103 | 2 |
| C4×Q16×C103 | 2 |
| #3299 | 103 |