Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
670 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20273049 | C2 | semidirect |
| 3. #20272642 | C2 | semidirect |
| 4. C53×#1464 | C2 | semidirect |
| 170. #1464 | D53 | semidirect |
| 194. C53 | #11503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277295 | 2 |
| #20273049 | 2 |
| #20272642 | 2 |
| C53×#1464 | 2 |
| #11503 | 53 |