Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
744 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20273163 | C2 | semidirect |
| 4. #20273059 | C2 | semidirect |
| 5. C4×#101×C53 | C2 | semidirect |
| 191. C4×#101 | D53 | semidirect |
| 222. C53 | #8368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811346 | 2 |
| #20273312 | 2 |
| #20273163 | 2 |
| #20273059 | 2 |
| C4×#101×C53 | 2 |
| #8368 | 53 |