Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
384 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 133 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×#15690801 | C2 | semidirect |
| 3. #20261045 | C2 | semidirect |
| 4. #20261041 | C2 | semidirect |
| 5. #20261038 | C2 | semidirect |
| 6. #20261034 | C2 | semidirect |
| 7. #20260778 | C2 | semidirect |
| 8. #20260758 | C2 | semidirect |
| 11. #428×C97 | C2 | semidirect |
| 136. C97 | #3080 | semidirect |
| 144. #428 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690801 | 2 |
| #20261203 | 2 |
| #20261045 | 2 |
| #20261041 | 2 |
| #20261038 | 2 |
| #20261034 | 2 |
| #20260778 | 2 |
| #20260758 | 2 |
| #20260737 | 2 |
| #20260734 | 2 |
| #428×C97 | 2 |
| #3080 | 97 |