Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1464 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 525 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 |
|---|---|---|
| 2. C22×Q8×D97 | C2 | semidirect |
| 3. C2×#15690842 | C2 | direct (N × H) |
| 4. C22×#13095501 | C2 | semidirect |
| 5. C22×#13095500 | C2 | semidirect |
| 6. C22×#13095498 | C2 | semidirect |
| 7. C22×#13095494 | C2 | semidirect |
| 8. C22×Q16×C97 | C2 | semidirect |
| 14. C2×Q8×D97 | C22 | semidirect |
| 20. #15690842 | C22 | direct (N × H) |
| 21. C2×#13095501 | C22 | semidirect |
| 22. C2×#13095500 | C22 | semidirect |
| 23. C2×#13095498 | C22 | semidirect |
| 24. C2×#13095494 | C22 | semidirect |
| 28. C2×Q16×C97 | C22 | semidirect |
| 38. Q8×D97 | C23 | semidirect |
| 48. #13095501 | C23 | semidirect |
| 49. #13095500 | C23 | semidirect |
| 50. #13095498 | C23 | semidirect |
| 51. #13095494 | C23 | semidirect |
| 60. Q16×C97 | C23 | semidirect |
| 89. C22×C97 | #137 | semidirect |
| 101. C2×C97 | C2×#137 | semidirect |
| 106. C97 | C22×#137 | semidirect |
| 111. C22×Q16 | D97 | semidirect |
| 130. C2×Q16 | C2×D97 | semidirect |
| 162. Q16 | C22×D97 | semidirect |
| 199. C22 | #15690842 | direct (N × H) |
| 209. C2 | C2×#15690842 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095512 | 2 |
| C22×Q8×D97 | 2 |
| C2×#15690842 | 2 |
| C22×#13095501 | 2 |
| C22×#13095500 | 2 |
| C22×#13095498 | 2 |
| C22×#13095494 | 2 |
| C22×Q16×C97 | 2 |
| C22×#137 | 97 |