Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
322 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20261044 | C2 | semidirect |
| 3. #20261041 | C2 | semidirect |
| 6. #20260944 | C2 | semidirect |
| 7. #20260943 | C2 | semidirect |
| 100. C97 | #3261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261345 | 2 |
| #20261044 | 2 |
| #20261041 | 2 |
| #20260991 | 2 |
| #20260976 | 2 |
| #20260944 | 2 |
| #20260943 | 2 |
| #20260761 | 2 |
| #467×C97 | 2 |
| #3261 | 97 |