Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20276481 | C2 | semidirect |
| 2. #20276343 | C2 | semidirect |
| 3. C2×#16810405 | C2 | semidirect |
| 4. #20276320 | C2 | semidirect |
| 24. #13133157 | D4 | semidirect |
| 159. C53 | #13201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276481 | 2 |
| #20276343 | 2 |
| C2×#16810405 | 2 |
| #20276320 | 2 |
| C53×#2930 | 2 |
| #13201 | 53 |