Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1188 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1188 conjugacy classes of subgroups — too many to draw. Only its 271 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. #20283179 | C2 | semidirect |
| 3. #20276389 | C2 | semidirect |
| 4. #20276378 | C2 | semidirect |
| 5. C53×#2884 | C2 | semidirect |
| 6. C2×#13133264 | C4 | semidirect |
| 11. #16811197 | C4 | semidirect |
| 14. C2×#13133215 | C4 | semidirect |
| 16. #41×Dic53 | C4 | semidirect |
| 176. #2884 | D53 | semidirect |
| 204. C53 | #33360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288496 | 2 |
| #20283179 | 2 |
| #20276389 | 2 |
| #20276378 | 2 |
| C53×#2884 | 2 |
| #33360 | 53 |