Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
612 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 170 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. #20261682 | C2 | semidirect |
| 7. #20261681 | C2 | semidirect |
| 8. #20261671 | C2 | semidirect |
| 27. #15690799 | C4 | semidirect |
| 28. #15690798 | C4 | semidirect |
| 29. #15690797 | C4 | semidirect |
| 30. #15690796 | C4 | semidirect |
| 33. #124×C97 | C4 | semidirect |
| 51. C2×Dic194 | C2×C4 | semidirect |
| 52. C2×Dic194 | C2×C4 | semidirect |
| 62. C22⋊Dic97 | C2×C4 | semidirect |
| 63. #13095488 | C2×C4 | semidirect |
| 64. #13095488 | C2×C4 | semidirect |
| 65. C4×Dic97 | C2×C4 | semidirect |
| 66. C4×Dic97 | C2×C4 | semidirect |
| 67. C2×Q8×C97 | C2×C4 | semidirect |
| 69. C22⋊C4×C97 | C2×C4 | semidirect |
| 70. C42×C97 | C2×C4 | semidirect |
| 139. C97 | #2326 | semidirect |
| 156. #124 | #87604 | semidirect |
| 178. C2×Q8 | C2×#87604 | semidirect |
| 203. C22⋊C4 | C2×#87604 | semidirect |
| 209. 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 |
| #20261682 | 2 |
| #20261681 | 2 |
| #20261671 | 2 |
| #124×D97 | 2 |
| #2326 | 97 |