Finite Group DatabasebetaFinite Group DatabasebetaOrder 1216.
190 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 190 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×#64515 | C2 | semidirect |
| 3. #10597338 | C2 | semidirect |
| 4. C19×#102 | C2 | semidirect |
| 5. #10597289 | C2 | semidirect |
| 6. #10597278 | C2 | semidirect |
| 7. #10597266 | C2 | semidirect |
| 12. D4×D19 | C4 | semidirect |
| 15. C2×C8×C19 | C22 | semidirect |
| 16. C4⋊C4×C19 | C22 | semidirect |
| 18. C4⋊Dic19 | C22 | semidirect |
| 20. C2×C19⋊C8 | C22 | semidirect |
| 70. #102 | D19 | semidirect |
| 71. C19 | #418 | semidirect |
| 81. C2×C8 | C2×D19 | semidirect |
| 83. C4⋊C4 | C2×D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D19 | 2 |
| C2×#64515 | 2 |
| #10597338 | 2 |
| C19×#102 | 2 |
| #10597289 | 2 |
| #10597278 | 2 |
| #10597266 | 2 |
| #418 | 19 |