Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
214 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 214 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. #20272913 | C2 | semidirect |
| 4. #20272912 | C2 | semidirect |
| 5. C53×#1422 | C2 | semidirect |
| 88. #1422 | D53 | direct (N × H) |
| 92. D53 | #1422 | direct (N × H) |
| 104. C53 | C2×#1422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M64×D53 | 2 |
| C4×C16×D53 | 2 |
| #20272913 | 2 |
| #20272912 | 2 |
| C53×#1422 | 2 |
| C2×#1422 | 53 |