Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
358 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20276489 | C2 | semidirect |
| 3. #20276487 | C2 | semidirect |
| 6. #20272811 | C2 | semidirect |
| 7. C53×#1382 | C2 | semidirect |
| 12. C2×#13133156 | C4 | semidirect |
| 13. C2×C16×D53 | C4 | semidirect |
| 141. #1382 | D53 | semidirect |
| 164. C53 | #12832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811039 | 2 |
| #20276489 | 2 |
| #20276487 | 2 |
| #20274762 | 2 |
| #20274758 | 2 |
| #20272811 | 2 |
| C53×#1382 | 2 |
| #12832 | 53 |