Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
164 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 55 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×#15690753 | C2 | semidirect |
| 2. C22×#13095486 | C2 | semidirect |
| 4. #20260562 | C2 | semidirect |
| 5. #20260539 | C2 | semidirect |
| 6. #20260535 | C2 | semidirect |
| 7. #467×C97 | C2 | semidirect |
| 28. #13095486 | D4 | semidirect |
| 59. C22×C97 | SD32 | semidirect |
| 76. C97 | #2217 | semidirect |
| 79. #467 | D97 | semidirect |
| 138. C22 | #15690753 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690753 | 2 |
| C22×#13095486 | 2 |
| #20260971 | 2 |
| #20260562 | 2 |
| #20260539 | 2 |
| #20260535 | 2 |
| #467×C97 | 2 |
| #2217 | 97 |