Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
338 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 23. #16810372 | C4 | semidirect |
| 24. #16810370 | C4 | semidirect |
| 25. #16810368 | C4 | semidirect |
| 26. C53×#333 | C4 | semidirect |
| 177. #333 | #6157 | semidirect |
| 182. C53 | #9579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290900 | 2 |
| C4⋊C8×#6157 | 2 |
| #20290283 | 2 |
| #20290025 | 2 |
| #20289607 | 2 |
| #20289542 | 2 |
| #20273369 | 2 |
| #9579 | 53 |