Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
362 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20272686 | C2 | semidirect |
| 75. Dic212 | M16 | semidirect |
| 137. C53 | #11664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic212 | 2 |
| #20273471 | 2 |
| #20272686 | 2 |
| C53×#2163 | 2 |
| #11664 | 53 |