Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
252 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 102 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. D4×#11719910 | C2 | semidirect |
| 2. #20289737 | C2 | semidirect |
| 3. D4⋊#11719910 | C2 | semidirect |
| 4. #20289628 | C2 | semidirect |
| 32. D8×C53 | C16 | semidirect |
| 49. D4×C53 | C2×C16 | semidirect |
| 57. C8×C53 | C2×C16 | semidirect |
| 92. C53 | #12062 | semidirect |
| 109. D8 | #11719910 | semidirect |
| 126. D4 | C2×#11719910 | semidirect |
| 138. C8 | C2×#11719910 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#11719910 | 2 |
| #20289737 | 2 |
| D4⋊#11719910 | 2 |
| #20289628 | 2 |
| D8×#88322 | 2 |
| #12062 | 53 |