Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
306 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 167 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. #20272634 | C2 | semidirect |
| 4. C8×#11719908 | C2 | semidirect |
| 5. C8×C16×C53 | C2 | semidirect |
| 47. C8×D53 | C16 | semidirect |
| 81. C8×C16 | D53 | semidirect |
| 97. C53 | #11410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276512 | 2 |
| C82×D53 | 2 |
| #20272634 | 2 |
| C8×#11719908 | 2 |
| C8×C16×C53 | 2 |
| #11410 | 53 |