Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
450 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 2. #20289651 | C2 | semidirect |
| 93. C2×C4×C53 | M32 | semidirect |
| 137. C53 | #11440 | semidirect |
| 217. C2×C4 | #13133291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290942 | 2 |
| #20289651 | 2 |
| C22×C4⋊#88322 | 2 |
| #11440 | 53 |