Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
542 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 193 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×#88322 | C2 | semidirect |
| 4. #20272566 | C2 | semidirect |
| 41. #100×C53 | C8 | semidirect |
| 57. M16×C53 | C2×C8 | semidirect |
| 99. #88322 | #100 | direct (N × H) |
| 142. C53 | C8×#100 | semidirect |
| 159. #100 | #88322 | direct (N × H) |
| 180. M16 | C2×#88322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#88322 | 2 |
| #20273036 | 2 |
| M16×#88322 | 2 |
| #20272566 | 2 |
| C4×#100×C53 | 2 |
| C8×#100 | 53 |