Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
252 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 95 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. C16×D212 | C2 | semidirect |
| 3. #20272779 | C2 | semidirect |
| 4. #20272671 | C2 | semidirect |
| 5. C53×#1312 | C2 | semidirect |
| 41. D424 | C16 | semidirect |
| 53. D212 | C2×C16 | semidirect |
| 59. C8×C53 | C2×C16 | semidirect |
| 77. #1312 | D53 | semidirect |
| 92. C53 | #12062 | semidirect |
| 137. C8 | C16×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×D212 | 2 |
| C8×D424 | 2 |
| #20272779 | 2 |
| #20272671 | 2 |
| C53×#1312 | 2 |
| #12062 | 53 |