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×#16811061 | C2 | semidirect |
| 2. C2×#16810894 | C2 | semidirect |
| 3. #20284387 | C2 | semidirect |
| 4. C2×#16810429 | C2 | semidirect |
| 5. C2×#16810423 | C2 | semidirect |
| 6. C2×#16810408 | C2 | semidirect |
| 7. C53×#1387 | C2 | semidirect |
| 50. C2×D424 | D4 | semidirect |
| 75. M32×C53 | D4 | semidirect |
| 78. #108×C53 | D4 | semidirect |
| 217. #1387 | D53 | semidirect |
| 249. C53 | #13307 | semidirect |
| 288. M32 | D212 | semidirect |
| 294. #108 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811061 | 2 |
| C2×#16810894 | 2 |
| #20284387 | 2 |
| C2×#16810429 | 2 |
| C2×#16810423 | 2 |
| C2×#16810408 | 2 |
| C53×#1387 | 2 |
| #13307 | 53 |