Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
948 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 112 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. C2×#16811540 | C2 | semidirect |
| 2. C2×#16811539 | C2 | semidirect |
| 3. #20290943 | C2 | semidirect |
| 4. #20290591 | C2 | semidirect |
| 6. C2×#13133292 | C22 | semidirect |
| 7. C2×#13133285 | C22 | semidirect |
| 16. C2×#13133239 | C4 | semidirect |
| 22. C2×Q16×D53 | C4 | semidirect |
| 24. C2×D8×D53 | C4 | semidirect |
| 26. C2×#135×C53 | C4 | semidirect |
| 127. Q16×C53 | C22⋊C4 | semidirect |
| 130. D8×C53 | C22⋊C4 | semidirect |
| 143. Dic212 | C22⋊C4 | semidirect |
| 145. D424 | C22⋊C4 | semidirect |
| 224. C2×D53 | #360 | semidirect |
| 255. C2×#135 | #6157 | semidirect |
| 268. C53 | #12735 | semidirect |
| 369. Q16 | C22⋊#6157 | semidirect |
| 378. D8 | C22⋊#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811540 | 2 |
| C2×#16811539 | 2 |
| #20290943 | 2 |
| #20290591 | 2 |
| C2×#135×D53 | 2 |
| #12735 | 53 |