Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
388 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20274835 | C2 | semidirect |
| 3. #20273411 | C2 | semidirect |
| 4. #20273410 | C2 | semidirect |
| 5. #20273222 | C2 | semidirect |
| 6. #20272584 | C2 | semidirect |
| 7. C53×#1505 | C2 | semidirect |
| 164. #1505 | D53 | semidirect |
| 191. C53 | #10513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286022 | 2 |
| #20274835 | 2 |
| #20273411 | 2 |
| #20273410 | 2 |
| #20273222 | 2 |
| #20272584 | 2 |
| C53×#1505 | 2 |
| #10513 | 53 |