Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
442 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 69 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. #20276970 | C2 | semidirect |
| 3. #20276761 | C2 | semidirect |
| 4. #20274081 | C2 | semidirect |
| 5. #20272675 | C2 | semidirect |
| 6. #20272669 | C2 | semidirect |
| 7. C53×#1361 | C2 | semidirect |
| 12. #16811003 | C22 | semidirect |
| 20. C4×#11719908 | C22 | semidirect |
| 23. C53×C4⋊C16 | C22 | semidirect |
| 24. C53×#335 | C22 | semidirect |
| 118. D212 | SD32 | semidirect |
| 154. #1361 | D53 | semidirect |
| 175. C4⋊C16 | C2×D53 | semidirect |
| 178. #335 | C2×D53 | semidirect |
| 180. C53 | #12320 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286390 | 2 |
| #20276970 | 2 |
| #20276761 | 2 |
| #20274081 | 2 |
| #20272675 | 2 |
| #20272669 | 2 |
| C53×#1361 | 2 |
| #12320 | 53 |