Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
366 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 1. #20286520 | C2 | semidirect |
| 2. #20276788 | C2 | semidirect |
| 3. #20274320 | C2 | semidirect |
| 4. #20272753 | C2 | semidirect |
| 5. #20272688 | C2 | semidirect |
| 6. #20272687 | C2 | semidirect |
| 7. C53×#2213 | C2 | semidirect |
| 141. #2213 | D53 | semidirect |
| 168. C53 | #12311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286520 | 2 |
| #20276788 | 2 |
| #20274320 | 2 |
| #20272753 | 2 |
| #20272688 | 2 |
| #20272687 | 2 |
| C53×#2213 | 2 |
| #12311 | 53 |