Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
834 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 179 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×#16811056 | C2 | semidirect |
| 2. #20285144 | C2 | semidirect |
| 3. #20276977 | C2 | semidirect |
| 4. #20276972 | C2 | semidirect |
| 5. #20276965 | C2 | semidirect |
| 6. C4×C16×D53 | C2 | semidirect |
| 7. C53×#2247 | C2 | semidirect |
| 42. C16×D53 | D4 | semidirect |
| 108. C4×C53 | #508 | semidirect |
| 117. #2247 | D53 | semidirect |
| 141. C53 | #33713 | semidirect |
| 226. C4 | #16811056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811056 | 2 |
| #20285144 | 2 |
| #20276977 | 2 |
| #20276972 | 2 |
| #20276965 | 2 |
| C4×C16×D53 | 2 |
| C53×#2247 | 2 |
| #33713 | 53 |