Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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×#15690830 | C2 | semidirect |
| 2. #20261406 | C2 | semidirect |
| 3. #20261109 | C2 | semidirect |
| 4. #20260966 | C2 | semidirect |
| 5. #20260942 | C2 | semidirect |
| 6. #20260930 | C2 | semidirect |
| 7. #20260895 | C2 | semidirect |
| 8. #20260880 | C2 | semidirect |
| 9. C4×#13095499 | C2 | semidirect |
| 10. D4×#11715895 | C2 | semidirect |
| 11. #547×C97 | C2 | semidirect |
| 52. #13095499 | D4 | semidirect |
| 129. C4×C97 | #135 | semidirect |
| 141. C97 | #3284 | semidirect |
| 144. #547 | D97 | semidirect |
| 272. C4 | #15690830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690830 | 2 |
| #20261406 | 2 |
| #20261109 | 2 |
| #20260966 | 2 |
| #20260942 | 2 |
| #20260930 | 2 |
| #20260895 | 2 |
| #20260880 | 2 |
| C4×#13095499 | 2 |
| D4×#11715895 | 2 |
| #547×C97 | 2 |
| #3284 | 97 |