Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
386 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20275490 | C2 | semidirect |
| 3. #20273399 | C2 | semidirect |
| 5. C2×#16810371 | C2 | semidirect |
| 7. C53×#1283 | C2 | semidirect |
| 171. #1283 | D53 | semidirect |
| 197. C53 | #10551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285109 | 2 |
| #20275490 | 2 |
| #20273399 | 2 |
| #20273390 | 2 |
| C2×#16810371 | 2 |
| #20273115 | 2 |
| C53×#1283 | 2 |
| #10551 | 53 |