Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
266 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 19. #16810398 | C4 | semidirect |
| 20. C4×#11719908 | C4 | semidirect |
| 21. C16×Dic53 | C4 | semidirect |
| 22. C53×#346 | C4 | semidirect |
| 123. #346 | #6157 | semidirect |
| 128. C53 | #12911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#368 | 2 |
| #20291066 | 2 |
| #20291062 | 2 |
| #20290634 | 2 |
| #20276313 | 2 |
| #12911 | 53 |