Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
424 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 424 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. #20276849 | C2 | semidirect |
| 3. #20274101 | C2 | semidirect |
| 4. #20272761 | C2 | semidirect |
| 5. #20272677 | C2 | semidirect |
| 6. #20272671 | C2 | semidirect |
| 7. C53×#2240 | C2 | semidirect |
| 17. C4⋊#11719908 | C22 | semidirect |
| 19. #16810376 | C22 | semidirect |
| 21. C53×#500 | C22 | semidirect |
| 24. C4×C16×C53 | C22 | semidirect |
| 87. D424 | SD16 | semidirect |
| 147. #2240 | D53 | semidirect |
| 161. #500 | C2×D53 | semidirect |
| 173. C4×C16 | C2×D53 | semidirect |
| 176. C53 | #12368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286390 | 2 |
| #20276849 | 2 |
| #20274101 | 2 |
| #20272761 | 2 |
| #20272677 | 2 |
| #20272671 | 2 |
| C53×#2240 | 2 |
| #12368 | 53 |