Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
244 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20276548 | C2 | semidirect |
| 2. C16×D212 | C2 | semidirect |
| 4. #20272785 | C2 | semidirect |
| 5. #20272671 | C2 | semidirect |
| 6. #20272671 | C2 | semidirect |
| 7. C53×#1311 | C2 | semidirect |
| 68. C16×C53 | D8 | semidirect |
| 81. D212 | M32 | semidirect |
| 115. #1311 | D53 | semidirect |
| 136. C53 | #12038 | semidirect |
| 184. C16 | D424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276548 | 2 |
| C16×D212 | 2 |
| C8×D424 | 2 |
| #20272785 | 2 |
| #20272671 | 2 |
| C53×#1311 | 2 |
| #12038 | 53 |