Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
390 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20276651 | C2 | semidirect |
| 3. #20276648 | C2 | semidirect |
| 5. #20272732 | C2 | semidirect |
| 7. C53×#1350 | C2 | semidirect |
| 172. #1350 | D53 | semidirect |
| 198. C53 | #12112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285605 | 2 |
| #20276651 | 2 |
| #20276648 | 2 |
| #20275837 | 2 |
| #20272732 | 2 |
| #20272640 | 2 |
| C53×#1350 | 2 |
| #12112 | 53 |