Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
406 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 3. #20289671 | C2 | direct (N × H) |
| 45. C2×Q16×C53 | C8 | semidirect |
| 61. Q16×C53 | C2×C8 | semidirect |
| 124. C2×C53 | #1332 | semidirect |
| 143. C53 | C2×#1332 | semidirect |
| 147. C2×Q16 | #88324 | semidirect |
| 183. Q16 | C2×#88324 | semidirect |
| 243. C2 | #20289671 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811509 | 2 |
| C2×#16811486 | 2 |
| #20289671 | 2 |
| C2×Q16×Dic53 | 2 |
| C2×#1332 | 53 |