Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
558 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#16811066 | C2 | semidirect |
| 3. C2×#16810434 | C2 | semidirect |
| 4. #20275586 | C2 | semidirect |
| 5. C53×#1377 | C2 | semidirect |
| 35. C2×Dic212 | D4 | semidirect |
| 55. M32×C53 | D4 | semidirect |
| 153. #1377 | D53 | semidirect |
| 175. C53 | #13342 | semidirect |
| 206. M32 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811066 | 2 |
| #20285161 | 2 |
| C2×#16810434 | 2 |
| #20275586 | 2 |
| C53×#1377 | 2 |
| #13342 | 53 |