Finite Group DatabasebetaFinite Group DatabasebetaOrder 1216.
198 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 1. C2×D4×D19 | C2 | semidirect |
| 2. C2×#64525 | C2 | semidirect |
| 3. C2×D152 | C2 | semidirect |
| 4. #10597341 | C2 | semidirect |
| 5. C19×#102 | C2 | semidirect |
| 6. (C2×D19)⋊C8 | C2 | semidirect |
| 7. #10597266 | C2 | semidirect |
| 15. C2×D76 | C22 | semidirect |
| 17. C2×C8×C19 | C22 | semidirect |
| 18. C4⋊C4×C19 | C22 | semidirect |
| 21. C2×C19⋊C8 | C22 | semidirect |
| 31. D4×C19 | D4 | semidirect |
| 40. D76 | D4 | semidirect |
| 58. C2×D19 | D8 | semidirect |
| 76. #102 | D19 | semidirect |
| 78. C19 | #447 | semidirect |
| 91. C2×C8 | C2×D19 | semidirect |
| 92. C4⋊C4 | C2×D19 | semidirect |
| 108. D4 | D76 | 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×#64525 | 2 |
| C2×D152 | 2 |
| #10597341 | 2 |
| C19×#102 | 2 |
| (C2×D19)⋊C8 | 2 |
| #10597266 | 2 |
| #447 | 19 |