Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
880 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 229 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. C2×#15690767 | C2 | semidirect |
| 3. C2×C4⋊C4×D97 | C2 | semidirect |
| 4. #20260642 | C2 | semidirect |
| 5. #20260637 | C2 | semidirect |
| 6. #20260636 | C2 | semidirect |
| 7. #20260613 | C2 | semidirect |
| 8. #20260594 | C2 | semidirect |
| 9. #391×C97 | C2 | semidirect |
| 12. C2×#13095512 | C4 | semidirect |
| 40. C2×D388 | C2×C4 | semidirect |
| 49. C2×C4×D97 | C2×C4 | semidirect |
| 61. C2×Q8×C97 | C2×C4 | semidirect |
| 103. C4×D97 | C22⋊C4 | semidirect |
| 134. C97 | #2311 | semidirect |
| 139. #391 | D97 | semidirect |
| 171. C2×Q8 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095512 | 2 |
| C2×#15690767 | 2 |
| C2×C4⋊C4×D97 | 2 |
| #20260642 | 2 |
| #20260637 | 2 |
| #20260636 | 2 |
| #20260613 | 2 |
| #20260594 | 2 |
| #391×C97 | 2 |
| #2311 | 97 |