Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
258 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 84 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. D8×#88324 | C2 | semidirect |
| 2. #20289746 | C2 | semidirect |
| 3. #20289669 | C2 | semidirect |
| 4. C16×#88324 | C2 | semidirect |
| 28. D16×C53 | C8 | semidirect |
| 38. D8×C53 | C2×C8 | semidirect |
| 45. C16×C53 | C2×C8 | semidirect |
| 59. #88324 | D16 | direct (N × H) |
| 93. C53 | C8×D16 | semidirect |
| 97. D16 | #88324 | direct (N × H) |
| 111. D8 | C2×#88324 | semidirect |
| 124. C16 | C2×#88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×#88324 | 2 |
| #20289746 | 2 |
| #20289669 | 2 |
| C16×#88324 | 2 |
| D16×Dic53 | 2 |
| C8×D16 | 53 |