Finite Group DatabasebetaFinite Group DatabasebetaOrder 1216.
122 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 2. C2×#64520 | C2 | semidirect |
| 3. C2×#64515 | C2 | semidirect |
| 4. C19×C22⋊C8 | C2 | semidirect |
| 5. (C2×D19)⋊C8 | C2 | semidirect |
| 6. Dic19⋊C8 | C2 | semidirect |
| 7. C8×Dic19 | C2 | semidirect |
| 36. C19⋊C8 | D4 | semidirect |
| 49. Dic19 | M16 | semidirect |
| 61. C22⋊C8 | D19 | semidirect |
| 63. C19 | #436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C22⋊D19 | 2 |
| C2×#64520 | 2 |
| C2×#64515 | 2 |
| C19×C22⋊C8 | 2 |
| (C2×D19)⋊C8 | 2 |
| Dic19⋊C8 | 2 |
| C8×Dic19 | 2 |
| #436 | 19 |