Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1152 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1152 conjugacy classes of subgroups — too many to draw. Only its 191 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×#16811234 | C2 | semidirect |
| 2. C2×#16810997 | C2 | semidirect |
| 3. C2×#16810988 | C2 | semidirect |
| 5. #20275717 | C2 | semidirect |
| 6. #20275679 | C2 | semidirect |
| 7. #20275068 | C2 | semidirect |
| 8. #20274484 | C2 | semidirect |
| 9. C53×#1960 | C2 | semidirect |
| 47. #13133209 | D4 | semidirect |
| 73. C4⋊Q8×C53 | D4 | semidirect |
| 195. #1960 | D53 | semidirect |
| 229. C53 | #25607 | semidirect |
| 241. C4⋊Q8 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811234 | 2 |
| C2×#16810997 | 2 |
| C2×#16810988 | 2 |
| #20280468 | 2 |
| #20275717 | 2 |
| #20275679 | 2 |
| #20275068 | 2 |
| #20274484 | 2 |
| C53×#1960 | 2 |
| #25607 | 53 |