Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20261073 | C2 | semidirect |
| 3. #20261027 | C2 | semidirect |
| 4. #20261022 | C2 | semidirect |
| 5. #20260942 | C2 | semidirect |
| 6. #20260937 | C2 | semidirect |
| 8. #20260840 | C2 | semidirect |
| 9. #20260833 | C2 | semidirect |
| 10. #20260792 | C2 | semidirect |
| 11. #533×C97 | C2 | semidirect |
| 137. C97 | #3116 | semidirect |
| 138. #533 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13095511 | 2 |
| #20261073 | 2 |
| #20261027 | 2 |
| #20261022 | 2 |
| #20260942 | 2 |
| #20260937 | 2 |
| #20260895 | 2 |
| #20260840 | 2 |
| #20260833 | 2 |
| #20260792 | 2 |
| #533×C97 | 2 |
| #3116 | 97 |