Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
284 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 61 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. #20276857 | C2 | semidirect |
| 4. #20274244 | C2 | semidirect |
| 6. #20272698 | C2 | semidirect |
| 7. C53×#1334 | C2 | semidirect |
| 143. #1334 | D53 | semidirect |
| 167. C53 | #12389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287792 | 2 |
| #20276952 | 2 |
| #20276857 | 2 |
| #20274244 | 2 |
| #20272757 | 2 |
| #20272698 | 2 |
| C53×#1334 | 2 |
| #12389 | 53 |