Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
226 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
| 59. #88322 | Q32 | direct (N × H) |
| 87. C53 | C8×Q32 | semidirect |
| 90. Q32 | #88322 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×#88322 | 2 |
| #20272787 | 2 |
| #20272679 | 2 |
| C16×#88322 | 2 |
| C4×Q32×C53 | 2 |
| C8×Q32 | 53 |