Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
656 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 213 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×#13095500 | C2 | semidirect |
| 2. C2×#15690810 | C2 | semidirect |
| 4. #20261108 | C2 | direct (N × H) |
| 5. C2×C4×C8×C97 | C2 | semidirect |
| 10. C2×#13095500 | C22 | semidirect |
| 12. #15690810 | C22 | semidirect |
| 18. C4×C8×C97 | C22 | semidirect |
| 33. C2×C8×C97 | D4 | semidirect |
| 41. C2×C4×C97 | SD16 | semidirect |
| 53. C8×C97 | C2×D4 | semidirect |
| 61. C4×C97 | C2×SD16 | semidirect |
| 64. C2×C97 | #492 | semidirect |
| 69. C97 | C2×#492 | semidirect |
| 74. C2×C4×C8 | D97 | semidirect |
| 87. C4×C8 | C2×D97 | semidirect |
| 101. C2×C8 | D388 | semidirect |
| 117. C2×C4 | #13095500 | semidirect |
| 122. C8 | C2×D388 | semidirect |
| 131. C4 | C2×#13095500 | semidirect |
| 134. C2 | #20261108 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095500 | 2 |
| C2×#15690810 | 2 |
| C2×#15690807 | 2 |
| #20261108 | 2 |
| C2×C4×C8×C97 | 2 |
| C2×#492 | 97 |