Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1492 conjugacy classes of subgroups; only the 754 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 754 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. #20261804 | C2 | semidirect |
| 2. #20261803 | C2 | semidirect |
| 3. #41×#87604 | C2 | semidirect |
| 4. C2×Q8×#87604 | C2 | semidirect |
| 14. #15690858 | C4 | semidirect |
| 15. #15690857 | C4 | semidirect |
| 18. 2−1+4×C97 | C4 | semidirect |
| 26. #13095512 | C2×C4 | semidirect |
| 27. #13095511 | C2×C4 | semidirect |
| 28. #13095510 | C2×C4 | semidirect |
| 29. C2×Dic194 | C2×C4 | semidirect |
| 30. Q8×D97 | C2×C4 | semidirect |
| 34. #41×C97 | C2×C4 | semidirect |
| 35. C2×Q8×C97 | C2×C4 | semidirect |
| 58. #87604 | 2−1+4 | direct (N × H) |
| 67. C97 | C4×2−1+4 | semidirect |
| 75. 2−1+4 | #87604 | direct (N × H) |
| 89. #41 | C2×#87604 | semidirect |
| 93. C2×Q8 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261804 | 2 |
| #20261803 | 2 |
| #41×#87604 | 2 |
| C2×Q8×#87604 | 2 |
| 2−1+4×D97 | 2 |
| C4×2−1+4 | 97 |