Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
322 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 219 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. #20272633 | C2 | semidirect |
| 44. C8×C53 | M32 | semidirect |
| 68. C53 | #11402 | semidirect |
| 101. C8 | #13133157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133157 | 2 |
| #20272633 | 2 |
| C2×C82×C53 | 2 |
| #11402 | 53 |