Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
500 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 217 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. C8×D388 | C2 | semidirect |
| 3. #20260800 | C2 | semidirect |
| 4. #20260788 | C2 | semidirect |
| 5. C22⋊C8×D97 | C2 | semidirect |
| 6. #431×C97 | C2 | semidirect |
| 9. C2×C8×D97 | 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 |
| 25. C2×D388 | C8 | semidirect |
| 49. C22×D97 | C2×C8 | semidirect |
| 53. C2×C4×C97 | C2×C8 | semidirect |
| 62. D388 | C2×C8 | semidirect |
| 63. D388 | C2×C8 | semidirect |
| 89. C97 | #2972 | semidirect |
| 94. #431 | D97 | semidirect |
| 107. C4⋊C8 | C2×D97 | semidirect |
| 112. C4×C8 | C2×D97 | semidirect |
| 148. C2×C4 | C8×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D388 | 2 |
| C8×D388 | 2 |
| #20260800 | 2 |
| #20260788 | 2 |
| C22⋊C8×D97 | 2 |
| #431×C97 | 2 |
| #2972 | 97 |