Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
376 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 3. #20261045 | C2 | semidirect |
| 4. #20261041 | C2 | semidirect |
| 5. #20261029 | C2 | semidirect |
| 6. #20261019 | C2 | semidirect |
| 47. C2×Dic194 | Q8 | semidirect |
| 130. C97 | #3078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261288 | 2 |
| C2×#15690775 | 2 |
| #20261045 | 2 |
| #20261041 | 2 |
| #20261029 | 2 |
| #20261019 | 2 |
| #20260775 | 2 |
| #20260758 | 2 |
| #20260745 | 2 |
| #20260743 | 2 |
| #428×C97 | 2 |
| #3078 | 97 |