Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20275491 | C2 | semidirect |
| 3. #20273485 | C2 | semidirect |
| 4. #20273465 | C2 | semidirect |
| 6. #20272590 | C2 | semidirect |
| 182. C53 | #10607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275556 | 2 |
| #20275491 | 2 |
| #20273485 | 2 |
| #20273465 | 2 |
| #20273383 | 2 |
| #20272590 | 2 |
| C2×C53×#331 | 2 |
| #10607 | 53 |