Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
652 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 182 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×Q8×#87604 | C2 | semidirect |
| 3. (C2×#87604)⋊Q8 | C2 | semidirect |
| 5. #20261685 | C2 | semidirect |
| 6. #20261679 | C2 | semidirect |
| 7. C22⋊C4×#87604 | C2 | semidirect |
| 8. C42×#87604 | C2 | semidirect |
| 27. #15690799 | C4 | semidirect |
| 28. #15690798 | C4 | semidirect |
| 29. #15690797 | C4 | semidirect |
| 30. #15690796 | C4 | semidirect |
| 33. #124×C97 | C4 | semidirect |
| 52. C2×Dic194 | C2×C4 | semidirect |
| 53. C2×Dic194 | C2×C4 | semidirect |
| 63. C22⋊Dic97 | C2×C4 | semidirect |
| 64. #13095488 | C2×C4 | semidirect |
| 65. #13095488 | C2×C4 | semidirect |
| 66. C4×Dic97 | C2×C4 | semidirect |
| 67. C4×Dic97 | C2×C4 | semidirect |
| 68. C2×Q8×C97 | C2×C4 | semidirect |
| 70. C22⋊C4×C97 | C2×C4 | semidirect |
| 71. C42×C97 | C2×C4 | semidirect |
| 125. #87604 | #124 | direct (N × H) |
| 140. C97 | C4×#124 | semidirect |
| 157. #124 | #87604 | direct (N × H) |
| 179. C2×Q8 | C2×#87604 | semidirect |
| 203. C22⋊C4 | C2×#87604 | semidirect |
| 211. C42 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#87604 | 2 |
| C2×D4×#87604 | 2 |
| (C2×#87604)⋊Q8 | 2 |
| #20261687 | 2 |
| #20261685 | 2 |
| #20261679 | 2 |
| C22⋊C4×#87604 | 2 |
| C42×#87604 | 2 |
| #124×D97 | 2 |
| C4×#124 | 97 |