Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
384 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 384 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. #20273476 | C2 | semidirect |
| 3. #20273317 | C2 | semidirect |
| 6. #20273005 | C2 | semidirect |
| 7. C53×#1470 | C2 | semidirect |
| 174. #1470 | D53 | semidirect |
| 205. C53 | #9790 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810980 | 2 |
| #20273476 | 2 |
| #20273317 | 2 |
| #20273314 | 2 |
| #20273066 | 2 |
| #20273005 | 2 |
| C53×#1470 | 2 |
| #9790 | 53 |