Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
346 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 53 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. #20286110 | C2 | semidirect |
| 2. #20276666 | C2 | semidirect |
| 3. #20275999 | C2 | semidirect |
| 4. #20272710 | C2 | semidirect |
| 5. #20272706 | C2 | semidirect |
| 6. #20272665 | C2 | semidirect |
| 197. C53 | #12175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286110 | 2 |
| #20276666 | 2 |
| #20275999 | 2 |
| #20272710 | 2 |
| #20272706 | 2 |
| #20272665 | 2 |
| C53×#2190 | 2 |
| #12175 | 53 |