Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
268 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 268 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. #20276965 | C2 | semidirect |
| 2. #20274070 | C2 | semidirect |
| 3. #20272787 | C2 | semidirect |
| 4. #20272762 | C2 | semidirect |
| 5. D4×C16×C53 | C2 | semidirect |
| 54. C16×C53 | D8 | semidirect |
| 58. D4×C53 | D16 | semidirect |
| 90. D4×C16 | D53 | semidirect |
| 110. C53 | #12430 | semidirect |
| 148. C16 | #11719922 | semidirect |
| 157. D4 | D848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276965 | 2 |
| #20274070 | 2 |
| #20272787 | 2 |
| #20272762 | 2 |
| D4×C16×C53 | 2 |
| #12430 | 53 |