Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
424 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20276940 | C2 | semidirect |
| 3. #20274101 | C2 | semidirect |
| 4. #20272762 | C2 | semidirect |
| 5. #20272676 | C2 | semidirect |
| 6. #20272669 | C2 | semidirect |
| 7. C53×#2224 | C2 | semidirect |
| 17. C4×#11719908 | C22 | semidirect |
| 18. #16810376 | C22 | semidirect |
| 20. C53×#500 | C22 | semidirect |
| 23. C53×C4⋊C16 | C22 | semidirect |
| 70. D8×C53 | SD16 | semidirect |
| 148. #2224 | D53 | semidirect |
| 161. #500 | C2×D53 | semidirect |
| 170. C4⋊C16 | C2×D53 | semidirect |
| 176. C53 | #12368 | semidirect |
| 227. D8 | #11719924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×D212 | 2 |
| #20276940 | 2 |
| #20274101 | 2 |
| #20272762 | 2 |
| #20272676 | 2 |
| #20272669 | 2 |
| C53×#2224 | 2 |
| #12368 | 53 |