Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
308 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 308 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 |
|---|---|---|
| 1. #20287675 | C2 | semidirect |
| 2. #20276956 | C2 | semidirect |
| 4. #20272768 | C2 | semidirect |
| 5. #20272697 | C2 | semidirect |
| 6. #20272681 | C2 | semidirect |
| 7. C53×#1688 | C2 | semidirect |
| 94. D424 | SD16 | semidirect |
| 144. #1688 | D53 | semidirect |
| 172. C53 | #12360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287675 | 2 |
| #20276956 | 2 |
| #20276747 | 2 |
| #20272768 | 2 |
| #20272697 | 2 |
| #20272681 | 2 |
| C53×#1688 | 2 |
| #12360 | 53 |