Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
210 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 49 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. #20261552 | C2 | semidirect |
| 2. #20261173 | C2 | semidirect |
| 3. C2×#15690755 | C2 | semidirect |
| 4. #20261005 | C2 | semidirect |
| 5. #20260552 | C2 | semidirect |
| 6. #20260543 | C2 | semidirect |
| 7. #350×C97 | C2 | semidirect |
| 91. C97 | #2193 | semidirect |
| 98. #350 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261552 | 2 |
| #20261173 | 2 |
| C2×#15690755 | 2 |
| #20261005 | 2 |
| #20260552 | 2 |
| #20260543 | 2 |
| #350×C97 | 2 |
| #2193 | 97 |