Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
730 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20274409 | C2 | semidirect |
| 2. #20272541 | C2 | semidirect |
| 3. #20272536 | C2 | semidirect |
| 51. C2×Q8×C53 | M16 | semidirect |
| 58. C2×D4×C53 | M16 | semidirect |
| 182. C53 | #7631 | semidirect |
| 217. C2×Q8 | #11719917 | semidirect |
| 224. C2×D4 | #11719917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274409 | 2 |
| #20272541 | 2 |
| #20272536 | 2 |
| C53×#2297 | 2 |
| #7631 | 53 |