Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
928 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 274 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 |
|---|---|---|
| 3. (C2×#87604)⋊Q8 | C2 | direct (N × H) |
| 13. C22×Dic194 | C4 | semidirect |
| 14. C22×Dic194 | C4 | semidirect |
| 17. C2×Q8×D97 | C4 | semidirect |
| 21. C22×Q8×C97 | C4 | semidirect |
| 26. C22×#87604 | Q8 | semidirect |
| 34. C2×Dic194 | C2×C4 | semidirect |
| 35. C2×Dic194 | C2×C4 | semidirect |
| 50. C2×Q8×C97 | C2×C4 | semidirect |
| 66. C2×#87604 | C2×Q8 | semidirect |
| 102. C2×C97 | #391 | semidirect |
| 105. D97 | #391 | semidirect |
| 110. C97 | C2×#391 | semidirect |
| 122. C22×Q8 | #87604 | semidirect |
| 141. C2×Q8 | C2×#87604 | semidirect |
| 216. C2 | (C2×#87604)⋊Q8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#87604 | 2 |
| C22×C4×#87604 | 2 |
| (C2×#87604)⋊Q8 | 2 |
| C2×(C2×#87604)⋊C4 | 2 |
| C22×Q8×D97 | 2 |
| C2×#391 | 97 |