Finite Group DatabasebetaFinite Group DatabasebetaOrder 1216.
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 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×C42×C19 | C2 | semidirect |
| 3. C2×#64520 | C2 | semidirect |
| 4. #10597262 | C2 | direct (N × H) |
| 10. #64541 | C4 | semidirect |
| 12. C2×D76 | C4 | semidirect |
| 14. C2×Dic38 | C4 | semidirect |
| 16. C42×C19 | C22 | semidirect |
| 18. #64520 | C22 | semidirect |
| 34. D76 | C2×C4 | semidirect |
| 38. Dic38 | C2×C4 | semidirect |
| 55. C2×C19 | #104 | semidirect |
| 60. C2×C42 | D19 | semidirect |
| 62. C19 | C2×#104 | semidirect |
| 77. C42 | C2×D19 | semidirect |
| 113. C2 | #10597262 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64541 | 2 |
| C2×C42×C19 | 2 |
| C2×#64520 | 2 |
| #10597262 | 2 |
| C2×#104 | 19 |