Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1074 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 219 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 |
|---|---|---|
| 2. C2×#16810918 | C2 | semidirect |
| 3. #20273836 | C2 | direct (N × H) |
| 5. C2×Q8⋊#88322 | C2 | semidirect |
| 12. #16810918 | C22 | semidirect |
| 18. Q8⋊#88322 | C22 | semidirect |
| 157. C2×C53 | #1630 | semidirect |
| 180. C53 | C2×#1630 | semidirect |
| 304. C2 | #20273836 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810995 | 2 |
| C2×#16810918 | 2 |
| #20273836 | 2 |
| C2×#16810367 | 2 |
| C2×Q8⋊#88322 | 2 |
| C2×C53×#559 | 2 |
| C2×#1630 | 53 |