Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. C2×#16811066 | C2 | semidirect |
| 3. C2×#16810882 | C2 | semidirect |
| 4. C2×#16810432 | C2 | semidirect |
| 5. #20276434 | C2 | semidirect |
| 6. C2×#16810404 | C2 | semidirect |
| 7. C53×#1386 | C2 | semidirect |
| 44. C2×Dic212 | D4 | semidirect |
| 75. M32×C53 | D4 | semidirect |
| 80. #106×C53 | D4 | semidirect |
| 212. #1386 | D53 | semidirect |
| 242. C53 | #13317 | semidirect |
| 283. M32 | D212 | semidirect |
| 289. #106 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811066 | 2 |
| #20284325 | 2 |
| C2×#16810882 | 2 |
| C2×#16810432 | 2 |
| #20276434 | 2 |
| C2×#16810404 | 2 |
| C53×#1386 | 2 |
| #13317 | 53 |