Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
232 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20260539 | C2 | direct (N × H) |
| 13. C2×Q16×C97 | C4 | semidirect |
| 28. Q16×C97 | C2×C4 | semidirect |
| 57. C2×C97 | #358 | semidirect |
| 62. C97 | C2×#358 | semidirect |
| 70. C2×Q16 | Dic97 | semidirect |
| 87. Q16 | C2×Dic97 | semidirect |
| 119. C2 | #20260539 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095486 | 2 |
| C2×#15690744 | 2 |
| #20260539 | 2 |
| C22×Q16×C97 | 2 |
| C2×#358 | 97 |