Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
280 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 62 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. #20291091 | C2 | semidirect |
| 2. #20291057 | C2 | semidirect |
| 3. #20289736 | C2 | semidirect |
| 4. #20289735 | C2 | semidirect |
| 5. #20289725 | C2 | semidirect |
| 6. #20289725 | C2 | semidirect |
| 166. C53 | #11991 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291091 | 2 |
| #20291057 | 2 |
| #20289736 | 2 |
| #20289735 | 2 |
| #20289725 | 2 |
| #20285342 | 2 |
| #11991 | 53 |