Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
146 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 25. Q16×C53 | C16 | semidirect |
| 75. C53 | #7069 | semidirect |
| 90. Q16 | #11719908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20272785 | 2 |
| C8×#11719908 | 2 |
| C8×Q16×C53 | 2 |
| #7069 | 53 |