Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 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. #20268325 | C2 | semidirect |
| 2. #20268193 | C2 | semidirect |
| 3. #20268175 | C2 | semidirect |
| 4. #20268146 | C2 | semidirect |
| 5. #20268049 | C2 | semidirect |
| 7. #20268037 | C2 | semidirect |
| 8. #20267904 | C2 | semidirect |
| 9. #20267899 | C2 | semidirect |
| 10. #20267893 | C2 | semidirect |
| 11. C4×M16×C103 | C2 | semidirect |
| 110. C103 | #3183 | semidirect |
| 121. C4×M16 | D103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268325 | 2 |
| #20268193 | 2 |
| #20268175 | 2 |
| #20268146 | 2 |
| #20268049 | 2 |
| #20268044 | 2 |
| #20268037 | 2 |
| #20267904 | 2 |
| #20267899 | 2 |
| #20267893 | 2 |
| C4×M16×C103 | 2 |
| #3183 | 103 |