Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1720 conjugacy classes of subgroups; only the 810 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 810 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. C22×#13095521 | C2 | semidirect |
| 2. C2×D97⋊M16 | C2 | direct (N × H) |
| 3. C22×#13095520 | C2 | semidirect |
| 4. C22×#13095519 | C2 | semidirect |
| 6. C2×#13095521 | C22 | semidirect |
| 7. D97⋊M16 | C22 | direct (N × H) |
| 8. C2×#13095520 | C22 | semidirect |
| 9. C2×#13095519 | C22 | semidirect |
| 10. C22×#11715897 | C22 | semidirect |
| 20. #13095521 | C23 | semidirect |
| 21. #13095520 | C23 | semidirect |
| 22. #13095519 | C23 | semidirect |
| 23. C2×#11715897 | C23 | semidirect |
| 49. C22×D97 | M16 | semidirect |
| 67. #11715897 | C24 | semidirect |
| 69. C22×C97 | C2×M16 | semidirect |
| 74. C2×D97 | C2×M16 | semidirect |
| 83. C2×C97 | C22×M16 | semidirect |
| 86. D97 | C22×M16 | semidirect |
| 88. C97 | C23×M16 | semidirect |
| 162. C22 | D97⋊M16 | direct (N × H) |
| 173. C2 | C2×D97⋊M16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095521 | 2 |
| C2×D97⋊M16 | 2 |
| C22×#13095520 | 2 |
| C22×#13095519 | 2 |
| C23×C4×D97 | 2 |
| C23×M16 | 97 |