Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
424 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20261048 | C2 | semidirect |
| 3. #20261030 | C2 | semidirect |
| 4. #20260935 | C2 | semidirect |
| 5. #20260874 | C2 | semidirect |
| 6. #20260833 | C2 | semidirect |
| 7. #20260792 | C2 | semidirect |
| 8. C2×C4×Q8×C97 | C2 | semidirect |
| 68. Q8×C97 | #41 | semidirect |
| 112. C97 | #3112 | semidirect |
| 114. C2×C4×Q8 | D97 | semidirect |
| 181. Q8 | #13095511 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261285 | 2 |
| #20261048 | 2 |
| #20261030 | 2 |
| #20260935 | 2 |
| #20260874 | 2 |
| #20260833 | 2 |
| #20260792 | 2 |
| C2×C4×Q8×C97 | 2 |
| #3112 | 97 |