Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
250 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20276968 | C2 | semidirect |
| 4. C4×C32×C53 | C2 | semidirect |
| 27. C32×C53 | D4 | semidirect |
| 59. C4×C53 | SD64 | semidirect |
| 66. C4×C32 | D53 | semidirect |
| 79. C53 | #13727 | semidirect |
| 93. C32 | D212 | semidirect |
| 125. C4 | #16810462 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810462 | 2 |
| #20276968 | 2 |
| #20276965 | 2 |
| C4×C32×C53 | 2 |
| #13727 | 53 |