Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
552 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20276290 | C2 | semidirect |
| 3. #20275884 | C2 | semidirect |
| 4. #20275385 | C2 | semidirect |
| 6. #20274861 | C2 | semidirect |
| 7. #20274818 | C2 | semidirect |
| 8. C4×#13133145 | C2 | semidirect |
| 9. C53×#1994 | C2 | semidirect |
| 157. #1994 | D53 | semidirect |
| 188. C53 | #29232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276290 | 2 |
| #20276002 | 2 |
| #20275884 | 2 |
| #20275385 | 2 |
| #20275215 | 2 |
| #20274861 | 2 |
| #20274818 | 2 |
| C4×#13133145 | 2 |
| C53×#1994 | 2 |
| #29232 | 53 |