Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
456 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 160 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 |
|---|---|---|
| 2. #14272203 | C2 | semidirect |
| 3. Q16×#1181 | C2 | semidirect |
| 15. C2×Q16×C29 | C4 | semidirect |
| 16. C2×#90785 | C4 | semidirect |
| 17. Q16×D29 | C4 | semidirect |
| 18. Q16×D29 | C4 | semidirect |
| 21. C2×Dic116 | C4 | semidirect |
| 115. C2×Q16 | #1181 | semidirect |
| 128. C29 | #2950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272231 | 2 |
| #14272203 | 2 |
| Q16×#1181 | 2 |
| #14272173 | 2 |
| #14272156 | 2 |
| #14272126 | 2 |
| C2×Q16×D29 | 2 |
| #2950 | 29 |