Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 3. #20274331 | C2 | semidirect |
| 5. #20272784 | C2 | semidirect |
| 6. #20272763 | C2 | semidirect |
| 7. C53×#1362 | C2 | semidirect |
| 95. #88322 | SD32 | semidirect |
| 115. #1362 | D53 | semidirect |
| 135. C53 | #12426 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276761 | 2 |
| #20276757 | 2 |
| #20274331 | 2 |
| #20273509 | 2 |
| #20272784 | 2 |
| #20272763 | 2 |
| C53×#1362 | 2 |
| #12426 | 53 |