Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 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×#15690831 | C2 | semidirect |
| 2. #20261405 | C2 | semidirect |
| 3. #20261388 | C2 | semidirect |
| 4. #20260961 | C2 | semidirect |
| 5. #20260942 | C2 | semidirect |
| 6. #20260927 | C2 | semidirect |
| 7. #20260894 | C2 | semidirect |
| 8. #20260879 | C2 | semidirect |
| 9. C4×#13095500 | C2 | semidirect |
| 10. C8×D388 | C2 | semidirect |
| 11. #492×C97 | C2 | semidirect |
| 57. #13095500 | D4 | semidirect |
| 127. C4×C97 | #135 | semidirect |
| 141. C97 | #3284 | semidirect |
| 145. #492 | D97 | semidirect |
| 272. C4 | #15690831 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690831 | 2 |
| #20261405 | 2 |
| #20261388 | 2 |
| #20260961 | 2 |
| #20260942 | 2 |
| #20260927 | 2 |
| #20260894 | 2 |
| #20260879 | 2 |
| C4×#13095500 | 2 |
| C8×D388 | 2 |
| #492×C97 | 2 |
| #3284 | 97 |