Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1206 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1206 conjugacy classes of subgroups — too many to draw. Only its 403 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. #20277077 | C2 | semidirect |
| 3. C4×#13133151 | C2 | semidirect |
| 4. #20274541 | C2 | semidirect |
| 5. C53×#1726 | C2 | semidirect |
| 8. C4×D424 | C4 | semidirect |
| 22. C4×D212 | C2×C4 | semidirect |
| 26. #13133151 | C2×C4 | semidirect |
| 27. #13133139 | C2×C4 | semidirect |
| 33. C4×C8×C53 | C2×C4 | semidirect |
| 54. D424 | C42 | semidirect |
| 89. #1726 | D53 | semidirect |
| 106. C53 | #20508 | semidirect |
| 121. C4×C8 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D424 | 2 |
| #20277077 | 2 |
| C4×#13133151 | 2 |
| #20274541 | 2 |
| C53×#1726 | 2 |
| #20508 | 53 |