Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
650 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20285630 | C2 | semidirect |
| 2. #20275539 | C2 | semidirect |
| 3. #20273275 | C2 | semidirect |
| 4. #20272560 | C2 | semidirect |
| 5. C53×#3150 | C2 | semidirect |
| 73. C2×C8×C53 | D8 | semidirect |
| 132. #3150 | D53 | semidirect |
| 156. C53 | #10218 | semidirect |
| 212. C2×C8 | #11719922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285630 | 2 |
| #20275539 | 2 |
| #20273275 | 2 |
| #20272560 | 2 |
| C53×#3150 | 2 |
| #10218 | 53 |