Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1134 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 191 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. #20285845 | C2 | semidirect |
| 3. #20279927 | C2 | semidirect |
| 4. #20273754 | C2 | semidirect |
| 5. #20273211 | C2 | semidirect |
| 6. C53×#1461 | C2 | semidirect |
| 179. #1461 | D53 | semidirect |
| 208. C53 | #18409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288486 | 2 |
| #20285845 | 2 |
| #20279927 | 2 |
| #20273754 | 2 |
| #20273211 | 2 |
| C53×#1461 | 2 |
| #18409 | 53 |