Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
540 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 189 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. #20267687 | C2 | semidirect |
| 4. #20267682 | C2 | semidirect |
| 5. #20267653 | C2 | semidirect |
| 6. #20267650 | C2 | semidirect |
| 7. #20267637 | C2 | semidirect |
| 8. C4×C4⋊C4×C103 | C2 | semidirect |
| 11. C4×D412 | C4 | semidirect |
| 97. C103 | #2319 | semidirect |
| 104. C4×C4⋊C4 | D103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D412 | 2 |
| #20267692 | 2 |
| #20267687 | 2 |
| #20267682 | 2 |
| #20267653 | 2 |
| #20267650 | 2 |
| #20267637 | 2 |
| C4×C4⋊C4×C103 | 2 |
| #2319 | 103 |