Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
376 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20261044 | C2 | semidirect |
| 5. #20261031 | C2 | semidirect |
| 6. #20261030 | C2 | semidirect |
| 7. #20261017 | C2 | semidirect |
| 11. #475×C97 | C2 | semidirect |
| 47. Q8×D97 | Q8 | semidirect |
| 131. C97 | #3078 | semidirect |
| 139. #475 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261290 | 2 |
| C4×Q8×D97 | 2 |
| #20261045 | 2 |
| #20261044 | 2 |
| #20261031 | 2 |
| #20261030 | 2 |
| #20261017 | 2 |
| #20260774 | 2 |
| #20260757 | 2 |
| #20260742 | 2 |
| #475×C97 | 2 |
| #3078 | 97 |