Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
242 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 76 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. Q16×#88324 | C2 | semidirect |
| 3. #20289749 | C2 | semidirect |
| 4. #20289671 | C2 | semidirect |
| 6. C16×#88324 | C2 | semidirect |
| 35. #13133160 | C8 | semidirect |
| 54. Q16×C53 | C2×C8 | semidirect |
| 67. #11719908 | C2×C8 | semidirect |
| 85. #88324 | SD32 | semidirect |
| 128. C53 | C8×SD32 | semidirect |
| 154. Q16 | D53⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×#88324 | 2 |
| #20290296 | 2 |
| #20289749 | 2 |
| #20289671 | 2 |
| #20289670 | 2 |
| C16×#88324 | 2 |
| #20276564 | 2 |
| C8×SD32 | 53 |