Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
542 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 3. M16×#88324 | C2 | semidirect |
| 4. #20289561 | C2 | semidirect |
| 41. #13133133 | C8 | semidirect |
| 70. M16×C53 | C2×C8 | semidirect |
| 77. #11719917 | C2×C8 | semidirect |
| 106. #88324 | #100 | semidirect |
| 153. C53 | C8×#100 | semidirect |
| 195. M16 | D53⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811651 | 2 |
| #20289956 | 2 |
| M16×#88324 | 2 |
| #20289561 | 2 |
| #20274506 | 2 |
| C8×#100 | 53 |