Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
402 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 402 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 |
|---|---|---|
| 1. #20291047 | C2 | semidirect |
| 2. C2×C4×#11719910 | C2 | semidirect |
| 3. D4⋊#11719910 | C2 | semidirect |
| 147. C53 | #11584 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291047 | 2 |
| C2×C4×#11719910 | 2 |
| D4⋊#11719910 | 2 |
| #20283427 | 2 |
| #11584 | 53 |