Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
308 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 14. Q8×Dic97 | C4 | semidirect |
| 16. C4×Dic194 | C4 | semidirect |
| 18. #15690775 | C4 | semidirect |
| 23. C4×Q8×C97 | C4 | semidirect |
| 64. Q8×C97 | C4⋊C4 | semidirect |
| 90. Dic194 | C4⋊C4 | semidirect |
| 103. C4×C97 | #103 | semidirect |
| 109. Dic97 | #103 | semidirect |
| 120. C97 | #1803 | semidirect |
| 133. C4×Q8 | #87604 | semidirect |
| 185. Q8 | C4⋊#87604 | semidirect |
| 229. C4 | #15690873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261736 | 2 |
| C2×#15690873 | 2 |
| #20261681 | 2 |
| #20261608 | 2 |
| C4×Q8×D97 | 2 |
| #1803 | 97 |