Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
206 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20272917 | C2 | semidirect |
| 4. #20272916 | C2 | semidirect |
| 5. C53×#1424 | C2 | semidirect |
| 9. C32×D53 | C4 | semidirect |
| 21. #13133123 | C2×C4 | semidirect |
| 24. C32×C53 | C2×C4 | semidirect |
| 61. #1424 | D53 | direct (N × H) |
| 64. D53 | #1424 | direct (N × H) |
| 73. C53 | C2×#1424 | semidirect |
| 84. C32 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D53 | 2 |
| #366×D53 | 2 |
| #20272917 | 2 |
| #20272916 | 2 |
| C53×#1424 | 2 |
| C2×#1424 | 53 |