Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 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. #20268606 | C2 | semidirect |
| 2. #20268605 | C2 | semidirect |
| 3. #20268169 | C2 | semidirect |
| 4. #20268066 | C2 | semidirect |
| 5. #20268064 | C2 | semidirect |
| 6. #20268063 | C2 | semidirect |
| 7. #20267974 | C2 | semidirect |
| 8. #20267972 | C2 | semidirect |
| 9. #20267908 | C2 | semidirect |
| 10. #20267906 | C2 | semidirect |
| 11. #578×C103 | C2 | semidirect |
| 147. C103 | #3293 | semidirect |
| 150. #578 | D103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268606 | 2 |
| #20268605 | 2 |
| #20268169 | 2 |
| #20268066 | 2 |
| #20268064 | 2 |
| #20268063 | 2 |
| #20267974 | 2 |
| #20267972 | 2 |
| #20267908 | 2 |
| #20267906 | 2 |
| #578×C103 | 2 |
| #3293 | 103 |