Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
258 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 119 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×#11719908 | C2 | semidirect |
| 2. #20272785 | C2 | semidirect |
| 3. D4⋊#11719908 | C2 | semidirect |
| 4. C8×#11719908 | C2 | semidirect |
| 33. D8×C53 | C16 | semidirect |
| 48. #11719908 | D8 | direct (N × H) |
| 51. D4×C53 | C2×C16 | semidirect |
| 62. C8×C53 | C2×C16 | semidirect |
| 95. C53 | C16×D8 | semidirect |
| 113. D8 | #11719908 | direct (N × H) |
| 131. D4 | C2×#11719908 | semidirect |
| 142. C8 | C2×#11719908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#11719908 | 2 |
| #20272785 | 2 |
| D4⋊#11719908 | 2 |
| C8×#11719908 | 2 |
| C8×D8×C53 | 2 |
| C16×D8 | 53 |