Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
688 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 688 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. #20261687 | C2 | semidirect |
| 2. #20261685 | C2 | semidirect |
| 3. #20261683 | C2 | semidirect |
| 4. #20261676 | C2 | semidirect |
| 6. C23×#87604 | C22 | semidirect |
| 7. C2×C4⋊#87604 | C22 | semidirect |
| 10. C2×C22⋊#87604 | C22 | semidirect |
| 11. C2×C4×#87604 | C22 | semidirect |
| 12. (C2×#87604)⋊C4 | C22 | semidirect |
| 15. #15690780 | C4 | semidirect |
| 16. #15690779 | C4 | semidirect |
| 17. #15690778 | C4 | semidirect |
| 19. #120×C97 | C4 | semidirect |
| 30. C23×D97 | C2×C4 | semidirect |
| 39. C22⋊Dic97 | C2×C4 | semidirect |
| 40. #13095488 | C2×C4 | semidirect |
| 41. C24×C97 | C2×C4 | semidirect |
| 43. C22⋊C4×C97 | C2×C4 | semidirect |
| 101. C97 | #2375 | semidirect |
| 113. #120 | #87604 | semidirect |
| 126. C24 | C2×#87604 | semidirect |
| 143. C22⋊C4 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261687 | 2 |
| #20261685 | 2 |
| #20261683 | 2 |
| #20261676 | 2 |
| #120×D97 | 2 |
| #2375 | 97 |