Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
588 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20277176 | C2 | semidirect |
| 3. #20275542 | C2 | semidirect |
| 4. #20273209 | C2 | semidirect |
| 5. #20273139 | C2 | semidirect |
| 6. #20272547 | C2 | semidirect |
| 7. C53×#1303 | C2 | semidirect |
| 12. #16810904 | C4 | semidirect |
| 13. #16810819 | C4 | semidirect |
| 128. C4×Dic53 | D8 | semidirect |
| 215. #1303 | D53 | semidirect |
| 245. C53 | #9237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284716 | 2 |
| #20277176 | 2 |
| #20275542 | 2 |
| #20273209 | 2 |
| #20273139 | 2 |
| #20272547 | 2 |
| C53×#1303 | 2 |
| #9237 | 53 |