Finite Group DatabasebetaFinite Group DatabasebetaOrder 1216.
108 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 35 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. #10597378 | C2 | semidirect |
| 2. C2×#64525 | C2 | semidirect |
| 3. #10597354 | C2 | semidirect |
| 4. #10597353 | C2 | semidirect |
| 5. C19×#100 | C2 | semidirect |
| 6. #10597280 | C2 | semidirect |
| 7. #10597279 | C2 | semidirect |
| 60. #100 | D19 | semidirect |
| 61. C19 | #472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10597378 | 2 |
| C2×#64525 | 2 |
| #10597354 | 2 |
| #10597353 | 2 |
| C19×#100 | 2 |
| #10597280 | 2 |
| #10597279 | 2 |
| #472 | 19 |