Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
688 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 189 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×#15690793 | C2 | semidirect |
| 3. #20260637 | C2 | semidirect |
| 4. #20260633 | C2 | semidirect |
| 5. #20260626 | C2 | semidirect |
| 6. #20260614 | C2 | semidirect |
| 7. #20260595 | C2 | semidirect |
| 8. C22×C42×C97 | C2 | semidirect |
| 50. C22×C4×C97 | D4 | semidirect |
| 107. C4×C97 | #123 | semidirect |
| 118. C97 | #2854 | semidirect |
| 121. C22×C42 | D97 | semidirect |
| 160. C22×C4 | D388 | semidirect |
| 227. C4 | #15690793 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690793 | 2 |
| C2×#15690784 | 2 |
| #20260637 | 2 |
| #20260633 | 2 |
| #20260626 | 2 |
| #20260614 | 2 |
| #20260595 | 2 |
| C22×C42×C97 | 2 |
| #2854 | 97 |