Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
554 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #20273396 | C2 | semidirect |
| 5. #20273110 | C2 | semidirect |
| 6. #20272618 | C2 | semidirect |
| 7. C53×#2568 | C2 | semidirect |
| 85. C2×Q8×C53 | SD16 | semidirect |
| 200. #2568 | D53 | semidirect |
| 234. C53 | #10244 | semidirect |
| 294. C2×Q8 | #11719924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285640 | 2 |
| #20284187 | 2 |
| #20273396 | 2 |
| #20273209 | 2 |
| #20273110 | 2 |
| #20272618 | 2 |
| C53×#2568 | 2 |
| #10244 | 53 |