Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
452 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 177 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. #20260814 | C2 | semidirect |
| 3. #20260812 | C2 | semidirect |
| 4. #20260788 | C2 | semidirect |
| 5. #20260697 | C2 | semidirect |
| 6. #431×C97 | C2 | semidirect |
| 9. C2×#13095494 | C22 | semidirect |
| 16. C4⋊#11715895 | C22 | semidirect |
| 18. #15690722 | C22 | semidirect |
| 19. C4×#11715895 | C22 | semidirect |
| 21. C4⋊C8×C97 | C22 | semidirect |
| 23. C4×C8×C97 | C22 | semidirect |
| 53. C2×C4×C97 | M16 | semidirect |
| 89. C97 | #2975 | semidirect |
| 94. #431 | D97 | semidirect |
| 107. C4⋊C8 | C2×D97 | semidirect |
| 112. C4×C8 | C2×D97 | semidirect |
| 148. C2×C4 | #13095494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D388 | 2 |
| #20260814 | 2 |
| #20260812 | 2 |
| #20260788 | 2 |
| #20260697 | 2 |
| #431×C97 | 2 |
| #2975 | 97 |