Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
424 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20275268 | C2 | semidirect |
| 5. #20275003 | C2 | semidirect |
| 6. #20272843 | C2 | semidirect |
| 7. C53×#2129 | C2 | semidirect |
| 190. #2129 | D53 | semidirect |
| 223. C53 | #13433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285582 | 2 |
| #20276364 | 2 |
| #20275268 | 2 |
| #20275240 | 2 |
| #20275003 | 2 |
| #20272843 | 2 |
| C53×#2129 | 2 |
| #13433 | 53 |