Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
362 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 3. #20272575 | C2 | semidirect |
| 4. #20272560 | C2 | semidirect |
| 5. C53×#1849 | C2 | semidirect |
| 108. #1849 | D53 | semidirect |
| 127. C53 | #10631 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275539 | 2 |
| #20273384 | 2 |
| #20272575 | 2 |
| #20272560 | 2 |
| C53×#1849 | 2 |
| #10631 | 53 |