Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
560 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 160 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×#87604)⋊Q8 | C2 | semidirect |
| 2. #20261685 | C2 | semidirect |
| 4. C22⋊C4×#87604 | C2 | semidirect |
| 5. #20261671 | C2 | semidirect |
| 19. #15690799 | C4 | semidirect |
| 20. #15690798 | C4 | semidirect |
| 21. #15690797 | C4 | semidirect |
| 22. #15690796 | C4 | semidirect |
| 25. #124×C97 | C4 | semidirect |
| 36. C2×Dic194 | C2×C4 | semidirect |
| 37. C2×Dic194 | C2×C4 | semidirect |
| 47. C22⋊Dic97 | C2×C4 | semidirect |
| 48. #13095488 | C2×C4 | semidirect |
| 49. #13095488 | C2×C4 | semidirect |
| 50. C4×Dic97 | C2×C4 | semidirect |
| 51. C4×Dic97 | C2×C4 | semidirect |
| 52. C2×Q8×C97 | C2×C4 | semidirect |
| 54. C22⋊C4×C97 | C2×C4 | semidirect |
| 55. C42×C97 | C2×C4 | semidirect |
| 113. C97 | #2372 | semidirect |
| 127. #124 | #87604 | semidirect |
| 144. C2×Q8 | C2×#87604 | semidirect |
| 163. C22⋊C4 | C2×#87604 | semidirect |
| 168. C42 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C2×#87604)⋊Q8 | 2 |
| #20261685 | 2 |
| #20261683 | 2 |
| C22⋊C4×#87604 | 2 |
| #20261671 | 2 |
| #124×D97 | 2 |
| #2372 | 97 |