Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 125 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×#15690833 | C2 | semidirect |
| 2. #20261388 | C2 | semidirect |
| 3. #20260973 | C2 | semidirect |
| 4. #20260937 | C2 | semidirect |
| 5. #20260896 | C2 | semidirect |
| 6. C4×D776 | C2 | semidirect |
| 7. C8×D388 | C2 | semidirect |
| 8. #494×C97 | C2 | semidirect |
| 38. D776 | D4 | semidirect |
| 85. C4×C97 | #135 | semidirect |
| 96. C97 | #3283 | semidirect |
| 99. #494 | D97 | semidirect |
| 183. C4 | #15690833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690833 | 2 |
| #20261388 | 2 |
| #20260973 | 2 |
| #20260937 | 2 |
| #20260896 | 2 |
| C4×D776 | 2 |
| C8×D388 | 2 |
| #494×C97 | 2 |
| #3283 | 97 |