Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
924 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 210 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×D4×#87604 | C2 | semidirect |
| 2. #20261687 | C2 | semidirect |
| 3. #20261681 | C2 | semidirect |
| 4. C42×#87604 | C2 | semidirect |
| 13. #15690807 | C4 | semidirect |
| 14. #15690806 | C4 | semidirect |
| 16. #127×C97 | C4 | semidirect |
| 24. C4×#87604 | D4 | semidirect |
| 26. C2×D388 | C2×C4 | semidirect |
| 27. C2×C22⋊D97 | C2×C4 | semidirect |
| 31. C4×Dic97 | C2×C4 | semidirect |
| 32. C2×D4×C97 | C2×C4 | semidirect |
| 33. C42×C97 | C2×C4 | semidirect |
| 60. #87604 | #127 | direct (N × H) |
| 61. C4×C97 | C4×D4 | semidirect |
| 62. Dic97 | C4×D4 | semidirect |
| 69. C97 | C4×#127 | semidirect |
| 79. #127 | #87604 | direct (N × H) |
| 91. C2×D4 | C2×#87604 | semidirect |
| 102. C42 | C2×#87604 | semidirect |
| 131. C4 | D4×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#87604 | 2 |
| #20261687 | 2 |
| #20261681 | 2 |
| C42×#87604 | 2 |
| #127×D97 | 2 |
| C4×#127 | 97 |