Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1010 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1010 conjugacy classes of subgroups — too many to draw. Only its 251 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. #20273855 | C2 | direct (N × H) |
| 71. C2×Q8×C53 | Q16 | semidirect |
| 109. Q8×C53 | C2×Q16 | semidirect |
| 148. C2×C53 | #1633 | semidirect |
| 171. C53 | C2×#1633 | semidirect |
| 219. C2×Q8 | #11719925 | semidirect |
| 256. Q8 | C2×#11719925 | semidirect |
| 286. C2 | #20273855 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811002 | 2 |
| C2×#16810918 | 2 |
| #20273855 | 2 |
| C2×#16810372 | 2 |
| C2×Q8⋊#88322 | 2 |
| C2×Q82×C53 | 2 |
| C2×#1633 | 53 |