Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
520 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 152 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. #20261682 | C2 | semidirect |
| 5. #20261679 | C2 | semidirect |
| 19. #15690799 | C4 | semidirect |
| 20. #15690798 | C4 | semidirect |
| 21. #15690797 | C4 | semidirect |
| 22. #15690796 | C4 | semidirect |
| 25. #124×C97 | C4 | semidirect |
| 37. C2×Dic194 | C2×C4 | semidirect |
| 38. C2×Dic194 | C2×C4 | semidirect |
| 48. C22⋊Dic97 | C2×C4 | semidirect |
| 49. #13095488 | C2×C4 | semidirect |
| 50. #13095488 | C2×C4 | semidirect |
| 51. C4×Dic97 | C2×C4 | semidirect |
| 52. C4×Dic97 | C2×C4 | semidirect |
| 53. C2×Q8×C97 | C2×C4 | semidirect |
| 55. C22⋊C4×C97 | C2×C4 | semidirect |
| 56. C42×C97 | C2×C4 | semidirect |
| 117. C97 | #2379 | semidirect |
| 131. #124 | #87604 | semidirect |
| 148. C2×Q8 | C2×#87604 | semidirect |
| 169. C22⋊C4 | C2×#87604 | semidirect |
| 173. 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 |
| #20261682 | 2 |
| #20261679 | 2 |
| #124×D97 | 2 |
| #2379 | 97 |