Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
338 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 71 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. D8×Dic106 | C2 | semidirect |
| 2. #20276939 | C2 | semidirect |
| 4. #20274076 | C2 | semidirect |
| 5. #20272771 | C2 | semidirect |
| 6. #20272695 | C2 | semidirect |
| 7. C53×#1331 | C2 | semidirect |
| 65. D8×C53 | SD16 | semidirect |
| 109. Dic106 | D16 | semidirect |
| 138. #1331 | D53 | semidirect |
| 161. C53 | #12352 | semidirect |
| 206. D8 | #11719913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×Dic106 | 2 |
| #20276939 | 2 |
| #20276750 | 2 |
| #20274076 | 2 |
| #20272771 | 2 |
| #20272695 | 2 |
| C53×#1331 | 2 |
| #12352 | 53 |