Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
274 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20260751 | C2 | semidirect |
| 3. #20260741 | C2 | semidirect |
| 4. #20260717 | C2 | semidirect |
| 5. C2×#15690726 | C2 | semidirect |
| 6. #20260507 | C2 | semidirect |
| 7. #430×C97 | C2 | semidirect |
| 111. C97 | #2048 | semidirect |
| 113. #430 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690838 | 2 |
| #20260751 | 2 |
| #20260741 | 2 |
| #20260717 | 2 |
| C2×#15690726 | 2 |
| #20260507 | 2 |
| #430×C97 | 2 |
| #2048 | 97 |