Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
434 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20286021 | C2 | semidirect |
| 2. #20276627 | C2 | semidirect |
| 3. #20276023 | C2 | semidirect |
| 4. #20272725 | C2 | semidirect |
| 5. #20272724 | C2 | semidirect |
| 6. #20272654 | C2 | semidirect |
| 7. C53×#2184 | C2 | semidirect |
| 149. C2×Dic53 | D16 | semidirect |
| 186. #2184 | D53 | semidirect |
| 218. C53 | #12158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286021 | 2 |
| #20276627 | 2 |
| #20276023 | 2 |
| #20272725 | 2 |
| #20272724 | 2 |
| #20272654 | 2 |
| C53×#2184 | 2 |
| #12158 | 53 |