Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
284 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 59 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. #20277035 | C2 | semidirect |
| 3. #20276823 | C2 | semidirect |
| 4. #20272903 | C2 | semidirect |
| 5. C53×#1400 | C2 | semidirect |
| 11. C2×Dic424 | C22 | semidirect |
| 15. #16810451 | C22 | semidirect |
| 18. C53×M64 | C22 | semidirect |
| 108. #1400 | D53 | semidirect |
| 123. M64 | C2×D53 | semidirect |
| 126. C53 | #13668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287851 | 2 |
| #20277035 | 2 |
| #20276823 | 2 |
| #20272903 | 2 |
| C53×#1400 | 2 |
| #13668 | 53 |