Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
154 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 59 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. #20260857 | C2 | semidirect |
| 2. #20260847 | C2 | semidirect |
| 3. #20260558 | C2 | semidirect |
| 4. #20260548 | C2 | semidirect |
| 5. #20260545 | C2 | semidirect |
| 6. #20260512 | C2 | semidirect |
| 18. SD32×C97 | C4 | semidirect |
| 19. D16×C97 | C4 | semidirect |
| 32. Q16×C97 | C2×C4 | semidirect |
| 36. D8×C97 | C2×C4 | semidirect |
| 38. C16×C97 | C2×C4 | semidirect |
| 69. C97 | AGL(1,ℤ/16) | semidirect |
| 81. SD32 | Dic97 | semidirect |
| 82. D16 | Dic97 | semidirect |
| 93. Q16 | C2×Dic97 | semidirect |
| 97. D8 | C2×Dic97 | semidirect |
| 107. C16 | C2×Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260857 | 2 |
| #20260847 | 2 |
| #20260558 | 2 |
| #20260548 | 2 |
| #20260545 | 2 |
| #20260512 | 2 |
| #509×C97 | 2 |
| AGL(1,ℤ/16) | 97 |