Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
444 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20283700 | C2 | semidirect |
| 3. #20273347 | C2 | semidirect |
| 4. #20273056 | C2 | semidirect |
| 5. #20272627 | C2 | semidirect |
| 6. #20272587 | C2 | semidirect |
| 7. C53×#1490 | C2 | semidirect |
| 202. #1490 | D53 | semidirect |
| 239. C53 | #9532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284853 | 2 |
| #20283700 | 2 |
| #20273347 | 2 |
| #20273056 | 2 |
| #20272627 | 2 |
| #20272587 | 2 |
| C53×#1490 | 2 |
| #9532 | 53 |