Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
772 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 202 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×D97⋊M16 | C2 | semidirect |
| 2. C2×#15690889 | C2 | semidirect |
| 3. #20261734 | C2 | direct (N × H) |
| 4. C2×#15690875 | C2 | semidirect |
| 6. C2×#13095521 | C22 | semidirect |
| 8. D97⋊M16 | C22 | semidirect |
| 12. #15690889 | C22 | semidirect |
| 15. C2×C4×#87604 | C22 | semidirect |
| 16. #15690875 | C22 | semidirect |
| 21. C2×#13095512 | C4 | semidirect |
| 22. C2×#13095512 | C4 | semidirect |
| 26. C22×D388 | C4 | semidirect |
| 29. C22×Q8×C97 | C4 | semidirect |
| 32. #13095521 | C23 | semidirect |
| 39. C4×#87604 | C23 | semidirect |
| 50. #13095512 | C2×C4 | semidirect |
| 59. C2×D388 | C2×C4 | semidirect |
| 76. C2×Q8×C97 | C2×C4 | semidirect |
| 145. C2×C97 | #421 | semidirect |
| 152. C97 | C2×#421 | semidirect |
| 166. C22×Q8 | #87604 | semidirect |
| 197. C2×Q8 | C2×#87604 | semidirect |
| 301. C2 | #20261734 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D97⋊M16 | 2 |
| C2×#15690889 | 2 |
| #20261734 | 2 |
| C2×#15690875 | 2 |
| C22×#13095512 | 2 |
| C2×#421 | 97 |