Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
682 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 682 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20275705 | C2 | semidirect |
| 3. #20273452 | C2 | semidirect |
| 4. #20273309 | C2 | semidirect |
| 7. C53×#1997 | C2 | semidirect |
| 217. #1997 | D53 | semidirect |
| 254. C53 | #8474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288599 | 2 |
| #20275705 | 2 |
| #20273452 | 2 |
| #20273309 | 2 |
| #20273155 | 2 |
| #20273152 | 2 |
| C53×#1997 | 2 |
| #8474 | 53 |