Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
320 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 106 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. #20291072 | C2 | semidirect |
| 2. C2×C4⋊#11719910 | C2 | semidirect |
| 3. Q8⋊#11719910 | C2 | semidirect |
| 4. D4⋊#11719910 | C2 | semidirect |
| 164. C53 | #11622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291072 | 2 |
| C2×C4⋊#11719910 | 2 |
| Q8⋊#11719910 | 2 |
| D4⋊#11719910 | 2 |
| #20283691 | 2 |
| #11622 | 53 |