Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1206 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1206 conjugacy classes of subgroups — too many to draw. Only its 403 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. #20277077 | C2 | semidirect |
| 3. C4×#13133150 | C2 | semidirect |
| 4. #20274543 | C2 | semidirect |
| 5. #20274540 | C2 | semidirect |
| 6. #20274402 | C2 | semidirect |
| 7. C53×#2275 | C2 | semidirect |
| 10. C4×#11719922 | C4 | semidirect |
| 31. C4×D212 | C2×C4 | semidirect |
| 35. #13133150 | C2×C4 | semidirect |
| 36. #13133138 | C2×C4 | semidirect |
| 37. #13133137 | C2×C4 | semidirect |
| 39. C4×#88322 | C2×C4 | semidirect |
| 44. C4×D4×C53 | C2×C4 | semidirect |
| 73. #11719922 | C42 | semidirect |
| 125. #2275 | D53 | semidirect |
| 152. C53 | #20508 | semidirect |
| 163. C4×D4 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11719922 | 2 |
| #20277077 | 2 |
| C4×#13133150 | 2 |
| #20274543 | 2 |
| #20274540 | 2 |
| #20274402 | 2 |
| C53×#2275 | 2 |
| #20508 | 53 |