Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
520 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 100 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. #20291522 | C2 | semidirect |
| 2. #20290012 | C2 | semidirect |
| 3. C2×#16811471 | C2 | semidirect |
| 4. #20289956 | C2 | semidirect |
| 5. #20289561 | C2 | semidirect |
| 6. #20289548 | C2 | semidirect |
| 99. C2×D212 | M16 | semidirect |
| 117. M16×C53 | M16 | semidirect |
| 258. C53 | #9097 | semidirect |
| 340. M16 | #11719936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291522 | 2 |
| #20290012 | 2 |
| C2×#16811471 | 2 |
| #20289956 | 2 |
| #20289561 | 2 |
| #20289548 | 2 |
| #20283522 | 2 |
| #9097 | 53 |