Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
296 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 9. #15690877 | C4 | semidirect |
| 10. C4⋊#11715897 | C4 | semidirect |
| 16. C4×#11715895 | C4 | semidirect |
| 17. C8×Dic97 | C4 | semidirect |
| 18. C8×Dic97 | C4 | semidirect |
| 19. C4×C8×C97 | C4 | semidirect |
| 24. C4⋊#87604 | C8 | direct (N × H) |
| 60. C8×C97 | C4⋊C4 | semidirect |
| 62. #11715895 | C4⋊C4 | semidirect |
| 70. C4×C97 | C4×C8 | semidirect |
| 74. Dic97 | C4×C8 | semidirect |
| 83. C97 | C8×C4⋊C4 | semidirect |
| 101. C4×C8 | #87604 | semidirect |
| 145. C8 | C4⋊#87604 | direct (N × H) |
| 157. C4 | C8×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261736 | 2 |
| C2×C8×#87604 | 2 |
| C4×C4⋊#87604 | 2 |
| #20261600 | 2 |
| C4×C8×D97 | 2 |
| C8×C4⋊C4 | 97 |