Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
324 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 1. #20276988 | C2 | semidirect |
| 2. #20276852 | C2 | semidirect |
| 3. #20274104 | C2 | semidirect |
| 4. #20272770 | C2 | semidirect |
| 5. #20272676 | C2 | semidirect |
| 6. D4⋊#11719908 | C2 | semidirect |
| 158. C53 | #12392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276988 | 2 |
| #20276852 | 2 |
| #20274104 | 2 |
| #20272770 | 2 |
| #20272676 | 2 |
| D4⋊#11719908 | 2 |
| C53×#3334 | 2 |
| #12392 | 53 |