Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1162 conjugacy classes of subgroups; only the 384 normal subgroups are shown.
This group has 1162 conjugacy classes of subgroups — too many to draw. Only its 384 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 |
|---|---|---|
| 1. #20291608 | C2 | semidirect |
| 2. #20289958 | C2 | semidirect |
| 37. C22×Q8×C53 | C8 | semidirect |
| 131. C53 | #17352 | semidirect |
| 134. C22×Q8 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291608 | 2 |
| #20289958 | 2 |
| #20289946 | 2 |
| C2×#16811101 | 2 |
| #17352 | 53 |