Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
466 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20272655 | C2 | semidirect |
| 4. #20272654 | C2 | semidirect |
| 5. C53×#1322 | C2 | semidirect |
| 62. C2×C4×D53 | C16 | semidirect |
| 102. C2×C4×C53 | C2×C16 | semidirect |
| 112. C2×Dic53 | C2×C16 | semidirect |
| 154. #1322 | D53 | direct (N × H) |
| 161. D53 | #1322 | direct (N × H) |
| 175. C53 | C2×#1322 | semidirect |
| 277. C2×C4 | C16×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C8×D53 | 2 |
| C22⋊C16×D53 | 2 |
| #20272655 | 2 |
| #20272654 | 2 |
| C53×#1322 | 2 |
| C2×#1322 | 53 |