Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
284 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 3. #20276858 | C2 | semidirect |
| 4. #20274244 | C2 | semidirect |
| 5. #20272696 | C2 | semidirect |
| 6. #20272684 | C2 | semidirect |
| 167. C53 | #12389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287797 | 2 |
| #20276951 | 2 |
| #20276858 | 2 |
| #20274244 | 2 |
| #20272696 | 2 |
| #20272684 | 2 |
| C53×#1360 | 2 |
| #12389 | 53 |