Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
422 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20285618 | C2 | semidirect |
| 2. #20276627 | C2 | semidirect |
| 3. #20275822 | C2 | semidirect |
| 4. #20272733 | C2 | semidirect |
| 5. #20272731 | C2 | semidirect |
| 6. #20272640 | C2 | semidirect |
| 7. C53×#2187 | C2 | semidirect |
| 179. #2187 | D53 | semidirect |
| 211. C53 | #12110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285618 | 2 |
| #20276627 | 2 |
| #20275822 | 2 |
| #20272733 | 2 |
| #20272731 | 2 |
| #20272640 | 2 |
| C53×#2187 | 2 |
| #12110 | 53 |