Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
316 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 316 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 |
|---|---|---|
| 3. #20276967 | C2 | semidirect |
| 4. #20274331 | C2 | semidirect |
| 6. #20272631 | C2 | semidirect |
| 7. C53×#2247 | C2 | semidirect |
| 96. #2247 | D53 | semidirect |
| 116. C53 | #12520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276972 | 2 |
| #20276971 | 2 |
| #20276967 | 2 |
| #20274331 | 2 |
| #20274322 | 2 |
| #20272631 | 2 |
| C53×#2247 | 2 |
| #12520 | 53 |