Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
412 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20276527 | C2 | semidirect |
| 3. #20272755 | C2 | semidirect |
| 4. #20272751 | C2 | semidirect |
| 5. C53×#2165 | C2 | semidirect |
| 16. #16810444 | C22 | semidirect |
| 20. C53×#364 | C22 | semidirect |
| 146. #2165 | D53 | semidirect |
| 167. #364 | C2×D53 | semidirect |
| 172. C53 | #11992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285167 | 2 |
| #20276527 | 2 |
| #20272755 | 2 |
| #20272751 | 2 |
| C53×#2165 | 2 |
| #11992 | 53 |