Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
658 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 2. #20272628 | C2 | semidirect |
| 3. C53×#1309 | C2 | semidirect |
| 78. #1309 | D53 | direct (N × H) |
| 82. D53 | #1309 | direct (N × H) |
| 90. C53 | C2×#1309 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #423×D53 | 2 |
| #20272628 | 2 |
| C53×#1309 | 2 |
| C2×#1309 | 53 |