Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
240 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20273600 | C2 | semidirect |
| 2. D8×#88322 | C2 | semidirect |
| 3. #20272789 | C2 | semidirect |
| 4. #20272676 | C2 | semidirect |
| 5. #20272676 | C2 | semidirect |
| 6. #20272634 | C2 | semidirect |
| 51. D8×C53 | M16 | semidirect |
| 134. C53 | #12073 | semidirect |
| 163. D8 | #11719917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20273600 | 2 |
| D8×#88322 | 2 |
| #20272789 | 2 |
| #20272676 | 2 |
| #20272634 | 2 |
| C4×D16×C53 | 2 |
| #12073 | 53 |