Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
400 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 181 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. #20260794 | C2 | semidirect |
| 3. #20260786 | C2 | semidirect |
| 4. #20260761 | C2 | semidirect |
| 6. C4×#13095495 | C2 | semidirect |
| 7. C2×C4×C8×C97 | C2 | semidirect |
| 78. C97 | #2922 | semidirect |
| 85. C2×C4×C8 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13095511 | 2 |
| #20260794 | 2 |
| #20260786 | 2 |
| #20260761 | 2 |
| #20260701 | 2 |
| C4×#13095495 | 2 |
| C2×C4×C8×C97 | 2 |
| #2922 | 97 |