Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
400 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 89 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. #364×D53 | C2 | semidirect |
| 3. #20272753 | C2 | semidirect |
| 4. #20272752 | C2 | semidirect |
| 5. C53×#1357 | C2 | semidirect |
| 103. #1357 | D53 | semidirect |
| 119. C53 | #11920 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285142 | 2 |
| #364×D53 | 2 |
| #20272753 | 2 |
| #20272752 | 2 |
| C53×#1357 | 2 |
| #11920 | 53 |