Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
382 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20276517 | C2 | semidirect |
| 3. #20276516 | C2 | semidirect |
| 4. #20272674 | C2 | semidirect |
| 5. #20272673 | C2 | semidirect |
| 6. #20272672 | C2 | semidirect |
| 7. C53×#1330 | C2 | semidirect |
| 18. C4⋊#11719908 | C22 | semidirect |
| 22. #16810399 | C22 | semidirect |
| 25. C53×C4⋊C16 | C22 | semidirect |
| 26. C53×#346 | C22 | semidirect |
| 170. #1330 | D53 | semidirect |
| 190. C4⋊C16 | C2×D53 | semidirect |
| 195. #346 | C2×D53 | semidirect |
| 196. C53 | #11636 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #436×D53 | 2 |
| #20276517 | 2 |
| #20276516 | 2 |
| #20272674 | 2 |
| #20272673 | 2 |
| #20272672 | 2 |
| C53×#1330 | 2 |
| #11636 | 53 |