Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
242 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20272778 | C2 | semidirect |
| 4. D4⋊#11719908 | C2 | semidirect |
| 5. #20272669 | C2 | semidirect |
| 6. #20272634 | C2 | semidirect |
| 7. C53×#2169 | C2 | semidirect |
| 83. D212 | M32 | semidirect |
| 109. #2169 | D53 | semidirect |
| 136. C53 | #12063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×D212 | 2 |
| C8×#11719922 | 2 |
| #20272778 | 2 |
| D4⋊#11719908 | 2 |
| #20272669 | 2 |
| #20272634 | 2 |
| C53×#2169 | 2 |
| #12063 | 53 |