Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
134 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 41 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. #20260782 | C2 | semidirect |
| 3. #20260559 | C2 | semidirect |
| 4. #20260558 | C2 | semidirect |
| 5. #20260548 | C2 | semidirect |
| 6. #20260516 | C2 | semidirect |
| 7. #361×C97 | C2 | semidirect |
| 66. C97 | #2238 | semidirect |
| 72. #361 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260985 | 2 |
| #20260782 | 2 |
| #20260559 | 2 |
| #20260558 | 2 |
| #20260548 | 2 |
| #20260516 | 2 |
| #361×C97 | 2 |
| #2238 | 97 |