Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
278 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 278 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 |
|---|---|---|
| 2. #20276864 | C2 | semidirect |
| 4. #20272770 | C2 | semidirect |
| 5. #20272680 | C2 | semidirect |
| 7. C53×#2254 | C2 | semidirect |
| 120. #2254 | D53 | semidirect |
| 147. C53 | #12397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287145 | 2 |
| #20276864 | 2 |
| #20274111 | 2 |
| #20272770 | 2 |
| #20272680 | 2 |
| #20272671 | 2 |
| C53×#2254 | 2 |
| #12397 | 53 |