Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
814 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 199 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 |
|---|---|---|
| 3. #20276968 | C2 | semidirect |
| 4. #20276967 | C2 | semidirect |
| 5. #20276966 | C2 | semidirect |
| 7. C53×#2247 | C2 | semidirect |
| 90. C4×D53 | Q32 | semidirect |
| 105. C4×C53 | C2×Q32 | semidirect |
| 110. Dic53 | C2×Q32 | semidirect |
| 116. #2247 | D53 | direct (N × H) |
| 120. D53 | #2247 | direct (N × H) |
| 138. C53 | C2×#2247 | semidirect |
| 221. C4 | Q32×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q32×D53 | 2 |
| #494×D53 | 2 |
| #20276968 | 2 |
| #20276967 | 2 |
| #20276966 | 2 |
| C4×C16×D53 | 2 |
| C53×#2247 | 2 |
| C2×#2247 | 53 |