Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
386 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20276489 | C2 | semidirect |
| 3. #20276436 | C2 | semidirect |
| 4. #20276434 | C2 | semidirect |
| 7. C53×#1389 | C2 | semidirect |
| 161. #1389 | D53 | semidirect |
| 184. C53 | #13405 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810899 | 2 |
| #20276489 | 2 |
| #20276436 | 2 |
| #20276434 | 2 |
| #20276344 | 2 |
| #20274758 | 2 |
| C53×#1389 | 2 |
| #13405 | 53 |