Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
944 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 119 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. C2×#16810762 | C2 | semidirect |
| 3. C2×#16810356 | C2 | semidirect |
| 4. #20272558 | C2 | semidirect |
| 5. C53×#1446 | C2 | semidirect |
| 38. C22⋊#88322 | D4 | semidirect |
| 43. C22×Q8×C53 | D4 | semidirect |
| 75. C22×C4×C53 | SD16 | semidirect |
| 177. #1446 | D53 | semidirect |
| 202. C53 | #9964 | semidirect |
| 207. C22×Q8 | D212 | semidirect |
| 269. C22×C4 | #11719924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810762 | 2 |
| #20280817 | 2 |
| C2×#16810356 | 2 |
| #20272558 | 2 |
| C53×#1446 | 2 |
| #9964 | 53 |