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. #20261050 | C2 | semidirect |
| 4. #20261027 | C2 | semidirect |
| 5. #20260936 | C2 | semidirect |
| 6. #20260935 | C2 | semidirect |
| 7. #20260875 | C2 | semidirect |
| 8. #20260838 | C2 | semidirect |
| 9. #20260834 | C2 | semidirect |
| 10. #20260791 | C2 | semidirect |
| 11. #477×C97 | C2 | semidirect |
| 87. Q8×C97 | #41 | semidirect |
| 113. Dic194 | #41 | semidirect |
| 141. C97 | #3112 | semidirect |
| 146. #477 | D97 | semidirect |
| 231. Q8 | #13095512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261286 | 2 |
| C4×Q8×D97 | 2 |
| #20261050 | 2 |
| #20261027 | 2 |
| #20260936 | 2 |
| #20260935 | 2 |
| #20260875 | 2 |
| #20260838 | 2 |
| #20260834 | 2 |
| #20260791 | 2 |
| #477×C97 | 2 |
| #3112 | 97 |