Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
302 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20276940 | C2 | semidirect |
| 3. #20274308 | C2 | semidirect |
| 4. #20272631 | C2 | semidirect |
| 5. C53×#2254 | C2 | semidirect |
| 42. C16×C53 | SD16 | semidirect |
| 65. #2254 | D53 | semidirect |
| 83. C53 | #12506 | semidirect |
| 111. C16 | #11719924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276965 | 2 |
| #20276940 | 2 |
| #20274308 | 2 |
| #20272631 | 2 |
| C53×#2254 | 2 |
| #12506 | 53 |