Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
528 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20276324 | C2 | semidirect |
| 3. C22⋊C16×D53 | C2 | semidirect |
| 4. #20272641 | C2 | semidirect |
| 5. #20272640 | C2 | semidirect |
| 6. #20272640 | C2 | semidirect |
| 7. C53×#1315 | C2 | semidirect |
| 20. C22⋊#11719908 | C22 | semidirect |
| 21. C22⋊#11719908 | C22 | semidirect |
| 25. C53×C22⋊C16 | C22 | semidirect |
| 26. C53×C22⋊C16 | C22 | semidirect |
| 206. #1315 | D53 | semidirect |
| 232. C22⋊C16 | C2×D53 | semidirect |
| 233. C22⋊C16 | C2×D53 | semidirect |
| 234. C53 | #11422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #408×D53 | 2 |
| #20276324 | 2 |
| C22⋊C16×D53 | 2 |
| #20272641 | 2 |
| #20272640 | 2 |
| C53×#1315 | 2 |
| #11422 | 53 |