Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
348 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×#15692931 | C2 | semidirect |
| 4. C2×C4×C103⋊C8 | C2 | semidirect |
| 6. #20267545 | C2 | semidirect |
| 7. #336×C103 | C2 | semidirect |
| 11. C2×#13110088 | C4 | semidirect |
| 16. (C2×D103)⋊C8 | C4 | semidirect |
| 60. C2×C4×C103 | M16 | semidirect |
| 80. C103⋊C8 | C22⋊C4 | semidirect |
| 105. C103 | #1753 | semidirect |
| 112. #336 | D103 | semidirect |
| 175. C2×C4 | #13110088 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13110088 | 2 |
| C2×(C2×D103)⋊C8 | 2 |
| C2×#15692931 | 2 |
| C2×C4×C103⋊C8 | 2 |
| C4×(C2×D103)⋊C4 | 2 |
| #20267545 | 2 |
| #336×C103 | 2 |
| #1753 | 103 |