Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
424 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20273059 | C2 | semidirect |
| 3. #20272660 | C2 | semidirect |
| 5. C53×#1467 | C2 | semidirect |
| 173. #1467 | D53 | semidirect |
| 199. C53 | #11534 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277422 | 2 |
| #20273059 | 2 |
| #20272660 | 2 |
| #20272646 | 2 |
| C53×#1467 | 2 |
| #11534 | 53 |