Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1202 conjugacy classes of subgroups; only the 355 normal subgroups are shown.
This group has 1202 conjugacy classes of subgroups — too many to draw. Only its 355 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. #20283796 | C2 | semidirect |
| 3. #20273274 | C2 | semidirect |
| 4. #20273209 | C2 | semidirect |
| 5. C53×#2351 | C2 | semidirect |
| 7. #16811295 | C4 | semidirect |
| 8. Q8×D212 | C4 | semidirect |
| 123. #2351 | D53 | semidirect |
| 147. C53 | #17618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288486 | 2 |
| #20283796 | 2 |
| #20273274 | 2 |
| #20273209 | 2 |
| C53×#2351 | 2 |
| #17618 | 53 |