Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20275655 | C2 | semidirect |
| 5. #20273145 | C2 | semidirect |
| 6. #20272611 | C2 | semidirect |
| 7. C53×#1281 | C2 | semidirect |
| 96. C2×C8×C53 | SD16 | semidirect |
| 186. #1281 | D53 | semidirect |
| 214. C53 | #9047 | semidirect |
| 291. C2×C8 | #11719913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284747 | 2 |
| #20283434 | 2 |
| #20275655 | 2 |
| #20273362 | 2 |
| #20273145 | 2 |
| #20272611 | 2 |
| C53×#1281 | 2 |
| #9047 | 53 |