Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20261366 | C2 | semidirect |
| 3. #20261044 | C2 | semidirect |
| 4. #20261033 | C2 | semidirect |
| 5. #20261023 | C2 | semidirect |
| 6. #20261018 | C2 | semidirect |
| 7. #20260777 | C2 | semidirect |
| 8. C2×#15690741 | C2 | semidirect |
| 9. #20260763 | C2 | semidirect |
| 64. #41×C97 | Q8 | semidirect |
| 124. C97 | #3084 | semidirect |
| 166. #41 | Dic194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261366 | 2 |
| #20261218 | 2 |
| #20261044 | 2 |
| #20261033 | 2 |
| #20261023 | 2 |
| #20261018 | 2 |
| #20260777 | 2 |
| C2×#15690741 | 2 |
| #20260763 | 2 |
| #20260731 | 2 |
| #417×C97 | 2 |
| #3084 | 97 |