Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
222 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 24. Q32×C53 | C8 | semidirect |
| 84. C53 | #12044 | semidirect |
| 87. Q32 | #88322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×#88322 | 2 |
| #20272789 | 2 |
| #20272679 | 2 |
| #20272631 | 2 |
| C4×Q32×C53 | 2 |
| #12044 | 53 |