Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
598 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20280575 | C2 | semidirect |
| 3. #20273338 | C2 | semidirect |
| 4. #20273262 | C2 | semidirect |
| 5. #20273162 | C2 | semidirect |
| 6. #20272581 | C2 | semidirect |
| 7. C53×#3112 | C2 | semidirect |
| 208. #3112 | D53 | semidirect |
| 245. C53 | #10020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285183 | 2 |
| #20280575 | 2 |
| #20273338 | 2 |
| #20273262 | 2 |
| #20273162 | 2 |
| #20272581 | 2 |
| C53×#3112 | 2 |
| #10020 | 53 |