Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
400 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 177 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. #20260793 | C2 | semidirect |
| 3. #20260785 | C2 | semidirect |
| 4. #20260763 | C2 | semidirect |
| 5. #20260761 | C2 | semidirect |
| 7. M16×Dic97 | C2 | semidirect |
| 8. C2×C8×Dic97 | C2 | semidirect |
| 94. C97 | #2922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic97 | 2 |
| #20260793 | 2 |
| #20260785 | 2 |
| #20260763 | 2 |
| #20260761 | 2 |
| #20260702 | 2 |
| M16×Dic97 | 2 |
| C2×C8×Dic97 | 2 |
| #408×C97 | 2 |
| #2922 | 97 |