Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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×#15690835 | C2 | semidirect |
| 2. C2×#15690807 | C2 | semidirect |
| 3. #20261125 | C2 | semidirect |
| 4. #20261111 | C2 | semidirect |
| 5. #20261109 | C2 | semidirect |
| 6. C4×#13095495 | C2 | semidirect |
| 7. #532×C97 | C2 | semidirect |
| 11. C2×#13095498 | C22 | semidirect |
| 12. C2×#13095496 | C22 | semidirect |
| 17. #15690721 | C22 | semidirect |
| 18. C4×#11715895 | C22 | semidirect |
| 20. C4⋊Q8×C97 | C22 | semidirect |
| 21. #127×C97 | C22 | semidirect |
| 22. #124×C97 | C22 | semidirect |
| 35. #13095495 | D4 | semidirect |
| 71. #11715895 | C2×D4 | semidirect |
| 83. C4×C97 | AGL(1,ℤ/8) | semidirect |
| 91. C97 | #3151 | semidirect |
| 93. #532 | D97 | semidirect |
| 106. C4⋊Q8 | C2×D97 | semidirect |
| 110. #127 | C2×D97 | semidirect |
| 111. #124 | C2×D97 | semidirect |
| 174. C4 | #15690835 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690835 | 2 |
| C2×#15690807 | 2 |
| #20261125 | 2 |
| #20261111 | 2 |
| #20261109 | 2 |
| C4×#13095495 | 2 |
| #532×C97 | 2 |
| #3151 | 97 |