Finite Group DatabasebetaFinite Group DatabasebetaOrder 1216.
158 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 55 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×C8×D19 | C2 | semidirect |
| 3. #10597338 | C2 | semidirect |
| 4. C19×#102 | C2 | semidirect |
| 5. #10597289 | C2 | semidirect |
| 6. #10597273 | C2 | semidirect |
| 7. #10597267 | C2 | semidirect |
| 12. #64543 | C4 | semidirect |
| 64. #102 | D19 | semidirect |
| 65. C19 | #416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64543 | 2 |
| C2×C8×D19 | 2 |
| #10597338 | 2 |
| C19×#102 | 2 |
| #10597289 | 2 |
| #10597273 | 2 |
| #10597267 | 2 |
| #416 | 19 |