Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
6046 conjugacy classes of subgroups; only the 1539 normal subgroups are shown.
This group has 6046 conjugacy classes of subgroups — too many to draw. Only its 1539 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×#16810542 | C2 | direct (N × H) |
| 9. #16810542 | C22 | direct (N × H) |
| 17. C23×Dic53 | Q8 | semidirect |
| 45. C22×Dic53 | C2×Q8 | semidirect |
| 65. C2×Dic53 | C22×Q8 | semidirect |
| 67. C22×C53 | #395 | semidirect |
| 81. C2×C53 | C2×#395 | semidirect |
| 94. C53 | C22×#395 | semidirect |
| 147. C22 | #16810542 | direct (N × H) |
| 157. C2 | C2×#16810542 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11719919 | 2 |
| C2×#16810542 | 2 |
| C22×#13133124 | 2 |
| C24×Q8×C53 | 2 |
| C22×#395 | 53 |