Finite Group DatabasebetaFinite Group DatabasebetaOrder 1216.
114 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 39 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. C4⋊C4×D19 | C2 | semidirect |
| 3. C19×#107 | C2 | semidirect |
| 4. #10597278 | C2 | semidirect |
| 5. (C2×D19)⋊C8 | C2 | semidirect |
| 6. #10597266 | C2 | semidirect |
| 7. #10597264 | C2 | semidirect |
| 56. #107 | D19 | semidirect |
| 60. C19 | #480 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10597341 | 2 |
| C4⋊C4×D19 | 2 |
| C19×#107 | 2 |
| #10597278 | 2 |
| (C2×D19)⋊C8 | 2 |
| #10597266 | 2 |
| #10597264 | 2 |
| #480 | 19 |