Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
406 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20276488 | C2 | semidirect |
| 4. #20275464 | C2 | semidirect |
| 5. #20272816 | C2 | semidirect |
| 6. #20272796 | C2 | semidirect |
| 25. C53×#360 | C4 | semidirect |
| 58. M32×C53 | C2×C4 | semidirect |
| 61. #106×C53 | C2×C4 | semidirect |
| 178. #360 | Dic53 | semidirect |
| 180. C53 | #12951 | semidirect |
| 203. M32 | C2×Dic53 | semidirect |
| 211. #106 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×Dic53 | 2 |
| #20276488 | 2 |
| #20276464 | 2 |
| #20275464 | 2 |
| #20272816 | 2 |
| #20272796 | 2 |
| C53×#2145 | 2 |
| #12951 | 53 |