Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
230 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 3. #20272791 | C2 | semidirect |
| 4. #20272790 | C2 | semidirect |
| 5. C53×#1373 | C2 | semidirect |
| 92. #1373 | D53 | direct (N × H) |
| 96. D53 | #1373 | direct (N × H) |
| 108. C53 | C2×#1373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #364×D53 | 2 |
| C4×C16×D53 | 2 |
| #20272791 | 2 |
| #20272790 | 2 |
| C53×#1373 | 2 |
| C2×#1373 | 53 |