Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
164 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20272913 | C2 | semidirect |
| 4. #20272850 | C2 | semidirect |
| 5. C53×#1422 | C2 | semidirect |
| 71. #1422 | D53 | semidirect |
| 86. C53 | #13643 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276310 | 2 |
| #20272913 | 2 |
| #20272854 | 2 |
| #20272850 | 2 |
| C53×#1422 | 2 |
| #13643 | 53 |