Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
348 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20272692 | C2 | semidirect |
| 4. #20272689 | C2 | semidirect |
| 5. C53×#1453 | C2 | semidirect |
| 14. #16810444 | C22 | semidirect |
| 20. C53×#322 | C22 | semidirect |
| 21. C82×C53 | C22 | semidirect |
| 122. #1453 | D53 | semidirect |
| 143. #322 | C2×D53 | semidirect |
| 144. C82 | C2×D53 | semidirect |
| 145. C53 | #11670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283626 | 2 |
| #20276527 | 2 |
| #20272692 | 2 |
| #20272689 | 2 |
| C53×#1453 | 2 |
| #11670 | 53 |