Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
534 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. C22⋊C16×D53 | C2 | semidirect |
| 3. #20272641 | C2 | semidirect |
| 4. #20272640 | C2 | semidirect |
| 5. C53×#1315 | C2 | semidirect |
| 15. C22⋊#11719908 | C22 | semidirect |
| 18. C53×C22⋊C16 | C22 | semidirect |
| 172. #1315 | D53 | direct (N × H) |
| 179. D53 | #1315 | direct (N × H) |
| 192. C22⋊C16 | C2×D53 | semidirect |
| 193. C53 | C2×#1315 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #408×D53 | 2 |
| C22⋊C16×D53 | 2 |
| #20272641 | 2 |
| #20272640 | 2 |
| C53×#1315 | 2 |
| C2×#1315 | 53 |