Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
238 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 3. #20289823 | C2 | semidirect |
| 4. #20289822 | C2 | semidirect |
| 5. #20289820 | C2 | semidirect |
| 6. C4×#13133267 | C2 | semidirect |
| 8. #16811556 | C4 | semidirect |
| 9. D53⋊C32 | C4 | semidirect |
| 100. C53 | #13549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811556 | 2 |
| C2×D53⋊C32 | 2 |
| #20289823 | 2 |
| #20289822 | 2 |
| #20289820 | 2 |
| C4×#13133267 | 2 |
| #20276313 | 2 |
| #13549 | 53 |