Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
372 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20273474 | C2 | semidirect |
| 3. #20272680 | C2 | semidirect |
| 4. #20272677 | C2 | semidirect |
| 5. C53×#2162 | C2 | semidirect |
| 91. Dic212 | M16 | semidirect |
| 93. D424 | M16 | semidirect |
| 147. #2162 | D53 | semidirect |
| 173. C53 | #11660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133239 | 2 |
| #20273474 | 2 |
| #20272680 | 2 |
| #20272677 | 2 |
| C53×#2162 | 2 |
| #11660 | 53 |