Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
186 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 25 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. #20272878 | C2 | semidirect |
| 3. C53×#1408 | C2 | semidirect |
| 4. #16811000 | C4 | semidirect |
| 8. C8×#88322 | C4 | semidirect |
| 69. #1408 | D53 | semidirect |
| 82. C53 | #7529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274329 | 2 |
| #20272878 | 2 |
| C53×#1408 | 2 |
| #7529 | 53 |