Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 197 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. #20275437 | C2 | semidirect |
| 4. #20275282 | C2 | semidirect |
| 6. #20274869 | C2 | semidirect |
| 7. C53×#1840 | C2 | semidirect |
| 118. #1840 | D53 | semidirect |
| 140. C53 | #23380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20278013 | 2 |
| #20275437 | 2 |
| #20275329 | 2 |
| #20275282 | 2 |
| #20274894 | 2 |
| #20274869 | 2 |
| C53×#1840 | 2 |
| #23380 | 53 |