Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
484 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 1. C2×#15690841 | C2 | semidirect |
| 3. #20260957 | C2 | semidirect |
| 4. #20260945 | C2 | semidirect |
| 5. #20260935 | C2 | semidirect |
| 6. #20260759 | C2 | semidirect |
| 7. #20260734 | C2 | semidirect |
| 8. C2×C4×Q8×C97 | C2 | semidirect |
| 52. C2×Q8×C97 | D4 | semidirect |
| 111. C4×C97 | #137 | semidirect |
| 121. C97 | #3037 | semidirect |
| 124. C2×C4×Q8 | D97 | semidirect |
| 160. C2×Q8 | D388 | semidirect |
| 233. C4 | #15690841 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690841 | 2 |
| #20261285 | 2 |
| #20260957 | 2 |
| #20260945 | 2 |
| #20260935 | 2 |
| #20260759 | 2 |
| #20260734 | 2 |
| C2×C4×Q8×C97 | 2 |
| #3037 | 97 |