Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
912 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 215 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. #20275011 | C2 | semidirect |
| 3. #20274858 | C2 | semidirect |
| 4. C53×#1839 | C2 | semidirect |
| 41. C42×C53 | M16 | semidirect |
| 76. #1839 | D53 | semidirect |
| 90. C53 | #23357 | semidirect |
| 122. C42 | #11719912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133214 | 2 |
| #20275011 | 2 |
| #20274858 | 2 |
| C53×#1839 | 2 |
| #23357 | 53 |