Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. #20276548 | C2 | semidirect |
| 2. #20274077 | C2 | semidirect |
| 4. #20272787 | C2 | semidirect |
| 5. #20272764 | C2 | semidirect |
| 6. #20272761 | C2 | semidirect |
| 7. C53×#2248 | C2 | semidirect |
| 72. C16×C53 | D8 | semidirect |
| 113. #2248 | D53 | semidirect |
| 140. C53 | #12435 | semidirect |
| 191. C16 | #11719922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276548 | 2 |
| #20274077 | 2 |
| #20274067 | 2 |
| #20272787 | 2 |
| #20272764 | 2 |
| #20272761 | 2 |
| C53×#2248 | 2 |
| #12435 | 53 |