Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
290 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 290 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. #20276751 | C2 | semidirect |
| 2. #20276747 | C2 | semidirect |
| 3. #20274329 | C2 | semidirect |
| 4. #20273509 | C2 | semidirect |
| 5. #20272784 | C2 | semidirect |
| 6. #20272760 | C2 | semidirect |
| 7. C53×#1361 | C2 | semidirect |
| 73. D424 | D8 | semidirect |
| 104. #88322 | D16 | semidirect |
| 128. #1361 | D53 | semidirect |
| 150. C53 | #12424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276751 | 2 |
| #20276747 | 2 |
| #20274329 | 2 |
| #20273509 | 2 |
| #20272784 | 2 |
| #20272760 | 2 |
| C53×#1361 | 2 |
| #12424 | 53 |