Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
646 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 646 conjugacy classes of subgroups — too many to draw. Only its 137 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. #20283624 | C2 | semidirect |
| 2. #20283362 | C2 | semidirect |
| 3. #20276294 | C2 | semidirect |
| 4. #20276022 | C2 | semidirect |
| 6. #20275425 | C2 | semidirect |
| 7. #20275214 | C2 | semidirect |
| 8. #20275074 | C2 | semidirect |
| 9. #20274999 | C2 | semidirect |
| 10. #20274862 | C2 | semidirect |
| 11. C53×#2098 | C2 | semidirect |
| 189. #2098 | D53 | semidirect |
| 229. C53 | #29387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283624 | 2 |
| #20283362 | 2 |
| #20276294 | 2 |
| #20276022 | 2 |
| #20275819 | 2 |
| #20275425 | 2 |
| #20275214 | 2 |
| #20275074 | 2 |
| #20274999 | 2 |
| #20274862 | 2 |
| C53×#2098 | 2 |
| #29387 | 53 |