Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
454 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 92 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. #20290830 | C2 | semidirect |
| 3. #20290273 | C2 | semidirect |
| 5. #20289607 | C2 | semidirect |
| 6. #20289547 | C2 | semidirect |
| 142. D212 | #108 | semidirect |
| 225. C53 | #8906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291456 | 2 |
| #20290830 | 2 |
| #20290273 | 2 |
| #20290041 | 2 |
| #20289607 | 2 |
| #20289547 | 2 |
| D4⋊C8×D53 | 2 |
| #8906 | 53 |