Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
252 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 75 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×#16810462 | C2 | semidirect |
| 2. C2×D1696 | C2 | semidirect |
| 3. #20276976 | C2 | semidirect |
| 4. #20276965 | C2 | semidirect |
| 5. C53×#1397 | C2 | semidirect |
| 33. C32×C53 | D4 | semidirect |
| 81. #1397 | D53 | semidirect |
| 97. C53 | #13729 | semidirect |
| 114. C32 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810462 | 2 |
| C2×D1696 | 2 |
| #20276976 | 2 |
| #20276965 | 2 |
| C53×#1397 | 2 |
| #13729 | 53 |