Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
486 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20276517 | C2 | semidirect |
| 3. #20273477 | C2 | semidirect |
| 4. #20272762 | C2 | semidirect |
| 5. #20272761 | C2 | semidirect |
| 6. #20272760 | C2 | semidirect |
| 7. C53×#1361 | C2 | semidirect |
| 17. C4⋊#11719908 | C22 | semidirect |
| 20. #16810376 | C22 | semidirect |
| 23. C53×C4⋊C16 | C22 | semidirect |
| 24. C53×#335 | C22 | semidirect |
| 159. #1361 | D53 | semidirect |
| 177. C4⋊C16 | C2×D53 | semidirect |
| 181. #335 | C2×D53 | semidirect |
| 183. C53 | #11964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #493×D53 | 2 |
| #20276517 | 2 |
| #20273477 | 2 |
| #20272762 | 2 |
| #20272761 | 2 |
| #20272760 | 2 |
| C53×#1361 | 2 |
| #11964 | 53 |