Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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. C4×Q8×D97 | C2 | semidirect |
| 3. #20261047 | C2 | semidirect |
| 4. #20261031 | C2 | semidirect |
| 5. #20261030 | C2 | semidirect |
| 6. #20260932 | C2 | semidirect |
| 7. #20260872 | C2 | semidirect |
| 8. #20260836 | C2 | semidirect |
| 9. #20260832 | C2 | semidirect |
| 10. #20260791 | C2 | semidirect |
| 11. #460×C97 | C2 | semidirect |
| 86. Q8×C97 | #41 | semidirect |
| 113. Dic194 | #41 | semidirect |
| 141. C97 | #3112 | semidirect |
| 148. #460 | D97 | semidirect |
| 231. Q8 | #13095510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261283 | 2 |
| C4×Q8×D97 | 2 |
| #20261047 | 2 |
| #20261031 | 2 |
| #20261030 | 2 |
| #20260932 | 2 |
| #20260872 | 2 |
| #20260836 | 2 |
| #20260832 | 2 |
| #20260791 | 2 |
| #460×C97 | 2 |
| #3112 | 97 |