Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
418 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 1. #20276410 | C2 | semidirect |
| 3. #20275268 | C2 | semidirect |
| 5. #20274934 | C2 | semidirect |
| 6. #20272838 | C2 | semidirect |
| 221. C53 | #13430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276410 | 2 |
| #20276407 | 2 |
| #20275268 | 2 |
| #20275263 | 2 |
| #20274934 | 2 |
| #20272838 | 2 |
| C53×#3200 | 2 |
| #13430 | 53 |