Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
306 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20276990 | C2 | semidirect |
| 3. #20276939 | C2 | semidirect |
| 4. #20274307 | C2 | semidirect |
| 5. C8×C16×C53 | C2 | semidirect |
| 45. C16×C53 | SD16 | semidirect |
| 57. C8×C53 | D16 | semidirect |
| 74. C8×C16 | D53 | semidirect |
| 89. C53 | #12503 | semidirect |
| 119. C16 | #11719913 | semidirect |
| 131. C8 | D848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276990 | 2 |
| #20276965 | 2 |
| #20276939 | 2 |
| #20274307 | 2 |
| C8×C16×C53 | 2 |
| #12503 | 53 |